TY - GEN AU - Gehér, György AU - Hruskova, Aranka AU - Titkos, Tamás AU - Virosztek, Dániel TI - Isometric rigidity of Wasserstein spaces over Euclidean spheres PY - 2023 UR - https://m2.mtmt.hu/api/publication/34131047 ID - 34131047 LA - English DB - MTMT ER - TY - JOUR AU - Gehér, György AU - Titkos, Tamás AU - Virosztek, Dániel TI - On isometries of Wasserstein spaces JF - RIMS KOKYUROKU BESSATSU J2 - RIMS KOKYUROKU BESSATSU VL - B93 PY - 2023 SP - 239 EP - 250 PG - 12 SN - 1881-6193 UR - https://m2.mtmt.hu/api/publication/33678624 ID - 33678624 LA - English DB - MTMT ER - TY - JOUR AU - Gehér, György AU - Titkos, Tamás AU - Virosztek, Dániel TI - Isometric rigidity of Wasserstein tori and spheres JF - MATHEMATIKA J2 - MATHEMATIKA VL - 69 PY - 2023 IS - 1 SP - 20 EP - 32 PG - 13 SN - 0025-5793 DO - 10.1112/mtk.12174 UR - https://m2.mtmt.hu/api/publication/33578758 ID - 33578758 N1 - Cited By :1 Export Date: 20 January 2023 Correspondence Address: Virosztek, D.; Alfréd Rényi Institute of Mathematics, Reáltanoda u. 13-15, Hungary; email: virosztek.daniel@renyi.hu Funding details: Leverhulme Trust, ECF‐2018‐125 Funding details: Magyar Tudományos Akadémia, MTA, K124152, KH129601, LP2021‐15/2021 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, K134944, PD128374 Funding text 1: Gehér was supported by the Leverhulme Trust Early Career Fellowship (ECF‐2018‐125), and also by the Hungarian National Research, Development and Innovation Office (Grant Number: K134944); Titkos was supported by the Hungarian National Research, Development and Innovation Office ‐ NKFIH (Grant Numbers: PD128374 and K134944) and by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences; Virosztek was supported by the Momentum program of the Hungarian Academy of Sciences under Grant Agreement Number: LP2021‐15/2021, and partially supported by the Hungarian National Research, Development and Innovation Office ‐ NKFIH (Grant Numbers: K124152 and KH129601). AB - We prove isometric rigidity for p-Wasserstein spaces over finite-dimensional tori and spheres for all p. We present a unified approach to proving rigidity that relies on the robust method of recovering measures from their Wasserstein potentials. © 2022 The Authors. The publishing rights in this article are licensed to University College London under an exclusive licence. Mathematika is published by the London Mathematical Society on behalf of University College London. LA - English DB - MTMT ER - TY - JOUR AU - Gehér, György AU - Pitrik, József AU - Titkos, Tamás AU - Virosztek, Dániel TI - Quantum Wasserstein isometries on the qubit state space JF - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS J2 - J MATH ANAL APPL VL - 522 PY - 2023 IS - 2 PG - 17 SN - 0022-247X DO - 10.1016/j.jmaa.2022.126955 UR - https://m2.mtmt.hu/api/publication/33578756 ID - 33578756 N1 - Export Date: 08 March 2024 AB - We describe Wasserstein isometries of the quantum bit state space with respect to distinguished cost operators. We derive a Wigner-type result for the cost operator involving all the Pauli matrices: in this case, the isometry group consists of unitary or anti-unitary conjugations. In the Bloch sphere model this means that the isometry group coincides with the classical symmetry group O(3). On the other hand, for the cost generated by the qubit ‘‘clock” and ‘‘shift” operators, we discovered non-surjective and non-injective isometries as well, beyond the regular ones. This phenomenon mirrors certain surprising properties of the quantum Wasserstein distance. © 2022 Elsevier Inc. LA - English DB - MTMT ER - TY - JOUR AU - Gehér, György AU - Titkos, Tamás AU - Virosztek, Dániel TI - The isometry group of Wasserstein spaces: the Hilbertian case JF - JOURNAL OF THE LONDON MATHEMATICAL SOCIETY J2 - J LOND MATH SOC VL - 106 PY - 2022 IS - 4 SP - 3836 EP - 3894 PG - 59 SN - 0024-6107 DO - 10.1112/jlms.12676 UR - https://m2.mtmt.hu/api/publication/31855431 ID - 31855431 N1 - Department of Mathematics and Statistics, University of Reading, Reading, United Kingdom Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary BBS University of Applied Sciences, Budapest, Hungary Institute of Science and Technology Austria, Klosterneuburg, Austria Cited By :2 Export Date: 20 January 2023 Correspondence Address: Gehér, G.P.; Department of Mathematics and Statistics, Whiteknights, P.O. Box 220, United Kingdom; email: gehergyuri@gmail.com Funding details: Institute of Science and Technology Austria, ISTA Funding details: Leverhulme Trust, ECF‐2018‐125 Funding details: Magyar Tudományos Akadémia, MTA Funding details: Horizon 2020, 846294, K124152, KH129601, LP2021‐15/2021 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, K115383, K134944, PD128374 Funding text 1: This paper is based on discussions made during research visits at the Institute of Science and Technology (IST) Austria, Klosterneuburg. We are grateful to the Erdős group for the warm hospitality. We are also grateful to Lajos Molnár for his comments on an earlier version of the manuscript and to László Erdős for his suggestions on the structure and highlights of this paper. We thank the anonymous referee for his/her valuable comments on the manuscript. Gehér was supported by the Leverhulme Trust Early Career Fellowship (ECF-2018-125), and also by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. K115383 and K134944). Titkos was supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. PD128374, grant no. K115383 and K134944), by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the ÚNKP-20-5-BGE-1 New National Excellence Program of the Ministry of Innovation and Technology. Virosztek was supported by the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, by the Momentum program of the Hungarian Academy of Sciences under grant agreement no. LP2021-15/2021, and partially supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grants no. K124152 and no. KH129601). Funding text 2: This paper is based on discussions made during research visits at the Institute of Science and Technology (IST) Austria, Klosterneuburg. We are grateful to the Erdős group for the warm hospitality. We are also grateful to Lajos Molnár for his comments on an earlier version of the manuscript and to László Erdős for his suggestions on the structure and highlights of this paper. We thank the anonymous referee for his/her valuable comments on the manuscript. Gehér was supported by the Leverhulme Trust Early Career Fellowship (ECF‐2018‐125), and also by the Hungarian National Research, Development and Innovation Office ‐ NKFIH (grant no. K115383 and K134944). Titkos was supported by the Hungarian National Research, Development and Innovation Office ‐ NKFIH (grant no. PD128374, grant no. K115383 and K134944), by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the ÚNKP‐20‐5‐BGE‐1 New National Excellence Program of the Ministry of Innovation and Technology. Virosztek was supported by the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska‐Curie Grant Agreement No. 846294, by the Momentum program of the Hungarian Academy of Sciences under grant agreement no. LP2021‐15/2021, and partially supported by the Hungarian National Research, Development and Innovation Office ‐ NKFIH (grants no. K124152 and no. KH129601). AB - Motivated by Kloeckner's result on the isometry group of the quadratic Wasserstein space (Formula presented.), we describe the isometry group (Formula presented.) for all parameters (Formula presented.) and for all separable real Hilbert spaces (Formula presented.). In particular, we show that (Formula presented.) is isometrically rigid for all Polish space (Formula presented.) whenever (Formula presented.). This is a consequence of our more general result: we prove that (Formula presented.) is isometrically rigid if (Formula presented.) is a complete separable metric space that satisfies the strict triangle inequality. Furthermore, we show that this latter rigidity result does not generalise to parameters (Formula presented.), by solving Kloeckner's problem affirmatively on the existence of mass-splitting isometries. As a byproduct of our methods, we also obtain the isometric rigidity of (Formula presented.) for all complete and separable ultrametric spaces (Formula presented.) and parameters (Formula presented.). © 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence. LA - English DB - MTMT ER - TY - JOUR AU - Brightmore, L AU - Gehér, György AU - Its, A R AU - Korepin, V E AU - Mezzadri, F AU - Mo, M Y AU - Virtanen, J A TI - Entanglement entropy of two disjoint intervals separated by one spin in a chain of free fermion JF - JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL J2 - J PHYS A-MATH THEOR VL - 53 PY - 2020 IS - 34 SP - 345303 SN - 1751-8113 DO - 10.1088/1751-8121/ab9cf2 UR - https://m2.mtmt.hu/api/publication/31846405 ID - 31846405 LA - English DB - MTMT ER - TY - JOUR AU - Gehér, György AU - Semrl, Peter TI - Coexistency on Hilbert Space Effect Algebras and a Characterisation of Its Symmetry Transformations JF - COMMUNICATIONS IN MATHEMATICAL PHYSICS J2 - COMMUN MATH PHYS VL - 379 PY - 2020 IS - 3 SP - 1077 EP - 1112 PG - 36 SN - 0010-3616 DO - 10.1007/s00220-020-03873-3 UR - https://m2.mtmt.hu/api/publication/31690523 ID - 31690523 AB - The Hilbert space effect algebra is a fundamental mathematical structure which is used to describe unsharp quantum measurements in Ludwig's formulation of quantum mechanics. Each effect represents a quantum (fuzzy) event. The relation of coexistence plays an important role in this theory, as it expresses when two quantum events can be measured together by applying a suitable apparatus. This paper's first goal is to answer a very natural question about this relation, namely, when two effects are coexistent with exactly the same effects? The other main aim is to describe all automorphisms of the effect algebra with respect to the relation of coexistence. In particular, we will see that they can differ quite a lot from usual standard automorphisms, which appear for instance in Ludwig's theorem. As a byproduct of our methods we also strengthen a theorem of Molnar. LA - English DB - MTMT ER - TY - JOUR AU - Gehér, György AU - Virosztek, Dániel AU - Titkos, Tamás TI - Isometric study of Wasserstein spaces - the real line, JF - TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY J2 - T AM MATH SOC VL - 373 PY - 2020 SP - 5855 EP - 5883 PG - 29 SN - 0002-9947 DO - 10.1090/tran/8113 UR - https://m2.mtmt.hu/api/publication/31161216 ID - 31161216 N1 - Department of Mathematics and Statistics, United Kingdom, University of Reading, Whiteknights, P.O. Box 220, Reading RG6 6AX, United Kingdom Alfréd Rényi Institute of Mathematics, Reáltanoda U. 13-15, Budapest, H-1053, Hungary Bbs University of Applied Sciences, Alkotmány U. 9, Budapest, H-1054, Hungary Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria Export Date: 4 January 2021 Funding details: National Research, Development and Innovation Office Funding details: Leverhulme Trust, ECF-2018-125 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, K115383 Funding details: National Research, Development and Innovation Office Funding details: Emberi Eroforrások Minisztériuma, EMMI Funding details: Magyar Tudományos Akadémia, MTA Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, PD128374, K115383 Funding details: National Research, Development and Innovation Office Funding details: Institute of Science and Technology Austria, IC1027FELL01 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, K124152, KH129601 Funding details: 846294 Funding text 1: The first author was supported by the Leverhulme Trust Early Career Fellowship (ECF-2018-125) and also by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. K115383). Funding text 2: The second author was supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. PD128374 and grant no. K115383), by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the ÚNKP-18-4-BGE-3 New National Excellence Program of the Ministry of Human Capacities. Funding text 3: The third author was supported by the ISTFELLOW program of the Institute of Science and Technology Austria (project code IC1027FELL01), by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grants no. K124152 and KH129601). Department of Mathematics and Statistics, United Kingdom, University of Reading, Whiteknights, P.O. Box 220, Reading RG6 6AX, United Kingdom Alfréd Rényi Institute of Mathematics, Reáltanoda U. 13-15, Budapest, H-1053, Hungary Bbs University of Applied Sciences, Alkotmány U. 9, Budapest, H-1054, Hungary Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria Export Date: 5 February 2021 Funding details: National Research, Development and Innovation Office Funding details: Leverhulme Trust, ECF-2018-125 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, K115383 Funding details: National Research, Development and Innovation Office Funding details: Emberi Eroforrások Minisztériuma, EMMI Funding details: Magyar Tudományos Akadémia, MTA Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, PD128374, K115383 Funding details: National Research, Development and Innovation Office Funding details: Institute of Science and Technology Austria, IC1027FELL01 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, K124152, KH129601 Funding details: 846294 Funding text 1: The first author was supported by the Leverhulme Trust Early Career Fellowship (ECF-2018-125) and also by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. K115383). Funding text 2: The second author was supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. PD128374 and grant no. K115383), by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the ÚNKP-18-4-BGE-3 New National Excellence Program of the Ministry of Human Capacities. Funding text 3: The third author was supported by the ISTFELLOW program of the Institute of Science and Technology Austria (project code IC1027FELL01), by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grants no. K124152 and KH129601). Department of Mathematics and Statistics, United Kingdom, University of Reading, Whiteknights, P.O. Box 220, Reading RG6 6AX, United Kingdom Alfréd Rényi Institute of Mathematics, Reáltanoda U. 13-15, Budapest, H-1053, Hungary Bbs University of Applied Sciences, Alkotmány U. 9, Budapest, H-1054, Hungary Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria Export Date: 31 May 2021 Funding details: Horizon 2020 Framework Programme, H2020, 846294 Funding details: Institute of Science and Technology Austria, IC1027FELL01 Funding details: Leverhulme Trust, ECF-2018-125 Funding details: Magyar Tudományos Akadémia, MTA Funding details: Emberi Eroforrások Minisztériuma, EMMI Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, K115383, K124152, KH129601, PD128374 Funding text 1: The third author was supported by the ISTFELLOW program of the Institute of Science and Technology Austria (project code IC1027FELL01), by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grants no. K124152 and KH129601). Funding text 2: The second author was supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. PD128374 and grant no. K115383), by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the ÚNKP-18-4-BGE-3 New National Excellence Program of the Ministry of Human Capacities. Funding text 3: The first author was supported by the Leverhulme Trust Early Career Fellowship (ECF-2018-125) and also by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. K115383). Funding Agency and Grant Number: Leverhulme Trust Early Career FellowshipLeverhulme Trust [ECF-2018-125]; Hungarian National Research, Development and Innovation Office - NKFIH [PD128374, K115383, K124152, KH129601]; Janos Bolyai Research Scholarship of the Hungarian Academy of SciencesHungarian Academy of Sciences; New National Excellence Program of the Ministry of Human Capacities [UNKP-18-4-BGE-3]; ISTFELLOW program of the Institute of Science and Technology Austria [IC1027FELL01]; European UnionEuropean Commission [846294] Funding text: The first author was supported by the Leverhulme Trust Early Career Fellowship (ECF-2018-125) and also by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. K115383).; The second author was supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. PD128374 and grant no. K115383), by the Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the UNKP-18-4-BGE-3 New National Excellence Program of the Ministry of Human Capacities.; The third author was supported by the ISTFELLOW program of the Institute of Science and Technology Austria (project code IC1027FELL01), by the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office -NKFIH (grants no. K124152 and KH129601). AB - The aim of this short paper is to offer a complete characterization of all (not necessarily surjective) isometric embeddings of the Wasserstein space Wp(X), where X is a countable discrete metric space and 0 LA - English DB - MTMT ER - TY - JOUR AU - Gehér, György TI - Symmetries of Projective Spaces and Spheres JF - INTERNATIONAL MATHEMATICS RESEARCH NOTICES J2 - INT MATH RES NOTICES VL - 2020 PY - 2020 IS - 7 SP - 2205 EP - 2240 PG - 36 SN - 1073-7928 DO - 10.1093/imrn/rny100 UR - https://m2.mtmt.hu/api/publication/31146441 ID - 31146441 AB - Let H be either a complex inner product space of dimension at least two or a real inner product space of dimension at least three, and let us fix an alpha is an element of(0, pi/2). The purpose of this paper is to characterise all bijective transformations on the projective space P(H) which preserve the quantum angle alpha (or Fubini-Study distance alpha) between lines in both directions. (Let us emphasise that we do not assume anything about the preservation of other quantum angles). For real inner product spaces and when H = C-2 we do this for every alpha, and when H is a complex inner product space of dimension at least three we describe the structure of such transformations for alpha <= pi/4. Our result immediately gives an Uhlhorn-type generalisation of Wigner's theorem on quantum mechanical symmetry transformations, that is considered to be a cornerstone of the mathematical foundations of quantum mechanics. Namely, under the above assumptions, every bijective map on the set of pure states of a quantum mechanical system that preserves the transition probability cos(2) alpha in both directions is a Wigner symmetry (thus automatically preserves all transition probabilities), except for the case when H = C-2 and alpha = pi/4 where an additional possibility occurs. (Note that the classical theorem of Uhlhorn is the solution for the alpha = pi/2 case). Usually in the literature, results which are connected to Wigner's theorem are discussed under the assumption of completeness of H; however, here we shall remove this unnecessary hypothesis in our investigation. Our main tool is a characterisation of bijective maps on unit spheres of real inner product spaces which preserve one spherical angle in both directions. LA - English DB - MTMT ER - TY - JOUR AU - Gehér, György AU - Tarcsay, Zsigmond AU - Titkos, Tamás TI - Maps preserving absolute continuity and singularity of positive operators JF - NEW YORK JOURNAL OF MATHEMATICS J2 - NEW YORK J MATH VL - 26 PY - 2020 SP - 129 EP - 137 PG - 9 SN - 1076-9803 UR - https://m2.mtmt.hu/api/publication/31033608 ID - 31033608 N1 - Department of Mathematics and Statistics, University of Reading, Whiteknights, P.O. Box 220, Reading, RG6 6AX, United Kingdom Department of Applied Analysis and Computational Mathematics, Eötvös Loránd University, étány 1/c., Budapest, H-1117, Hungary Alfréd Rényi Institute of Mathematics, Reáltanoda u. 13-15., Budapest, H-1053, Hungary BBS University of Applied Sciences, Alkot-mány u. 9., Budapest, H-1054, Hungary Export Date: 18 August 2020 Funding details: Magyar Tudományos Akadémia, MTA Funding details: Leverhulme Trust, ECF-2018-125 Funding details: PD128374, K115383 Funding details: 308015 Funding text 1: Gy. P. Gehér was supported by the Leverhulme Trust Early Career Fellowship (ECF-2018-125), and also by the Hungarian National Research, Development and Innovation Office (Grant no. K115383). Zs. Tarcsay was supported by DAAD-TEMPUS Cooperation Project “Harmonic Analysis and Extremal Problems” (grant no. 308015) and by Thematic Excellence Programme, Industry and Digitization Subprogramme, NRDI Office, 2019. T. Titkos was supported by the Hungarian National Research, Development and Innovation Office NKFIH (grant no. PD128374 and grant no. K115383), by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the ÚNKP-19-4-BGE-1 New National Excellence Program of the Ministry for Innovation and Technology. Funding Agency and Grant Number: Leverhulme TrustLeverhulme Trust [ECF-2018-125]; Hungarian National Research, Development and Innovation Office [K115383]; DAAD-TEMPUS Cooperation Project "Harmonic Analysis and Extremal Problems" [308015]; Thematic Excellence Programme, Industry and Digitization Subprogramme, NRDI Office, 2019; Hungarian National Research, Development and Innovation Office NKFIH [K115383, PD128374]; Janos Bolyai Research Scholarship of the Hungarian Academy of SciencesHungarian Academy of Sciences; Ministry for Innovation and Technology [UNKP-19-4-BGE-1] Funding text: Gy. P. Geher was supported by the Leverhulme Trust Early Career Fellowship (ECF-2018-125), and also by the Hungarian National Research, Development and Innovation Office (Grant no. K115383). Zs. Tarcsay was supported by DAAD-TEMPUS Cooperation Project "Harmonic Analysis and Extremal Problems" (grant no. 308015) and by Thematic Excellence Programme, Industry and Digitization Subprogramme, NRDI Office, 2019. T. Titkos was supported by the Hungarian National Research, Development and Innovation Office NKFIH (grant no. PD128374 and grant no. K115383), by the Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the UNKP-19-4-BGE-1 New National Excellence Program of the Ministry for Innovation and Technology. Department of Mathematics and Statistics, University of Reading, Whiteknights, P.O. Box 220, Reading, RG6 6AX, United Kingdom Department of Applied Analysis and Computational Mathematics, Eötvös Loránd University, étány 1/c., Budapest, H-1117, Hungary Alfréd Rényi Institute of Mathematics, Reáltanoda u. 13-15., Budapest, H-1053, Hungary BBS University of Applied Sciences, Alkot-mány u. 9., Budapest, H-1054, Hungary Export Date: 5 February 2021 Funding details: National Research, Development and Innovation Office, K115383 Funding details: Magyar Tudományos Akadémia, MTA Funding details: Ministry for Innovation and Technology Funding details: Leverhulme Trust, ECF-2018-125 Funding details: PD128374 Funding details: 308015 Funding text 1: Gy. P. Gehér was supported by the Leverhulme Trust Early Career Fellowship (ECF-2018-125), and also by the Hungarian National Research, Development and Innovation Office (Grant no. K115383). Zs. Tarcsay was supported by DAAD-TEMPUS Cooperation Project “Harmonic Analysis and Extremal Problems” (grant no. 308015) and by Thematic Excellence Programme, Industry and Digitization Subprogramme, NRDI Office, 2019. T. Titkos was supported by the Hungarian National Research, Development and Innovation Office NKFIH (grant no. PD128374 and grant no. K115383), by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the ÚNKP-19-4-BGE-1 New National Excellence Program of the Ministry for Innovation and Technology. LA - English DB - MTMT ER -