TY - JOUR AU - Prokaj, Rudolf Dániel AU - Simon, Károly TI - Special families of piecewise linear iterated function systems JF - DYNAMIC SYSTEMS AND APPLICATIONS J2 - DYNAM SYST APPL VL - accepted PY - 2024 SP - & SN - 1056-2176 UR - https://m2.mtmt.hu/api/publication/34767759 ID - 34767759 AB - This paper investigates the dimension theory of some families of continuous piecewise linear iterated function systems. For one family, we show that the Hausdorff dimension of the attractor is equal to the exponential growth rate obtained from the most natural covering system. We also prove that for Lebesgue typical parameters, the 1-dimensional Lebesgue measure of the underlying attractor is positive, if this number is bigger than 1 and all the contraction ratios are positive. LA - English DB - MTMT ER - TY - JOUR AU - Mosonyi, Milán AU - Bunth, Gergely AU - Vrana, Péter TI - Geometric relative entropies and barycentric Rényi divergences JF - LINEAR ALGEBRA AND ITS APPLICATIONS J2 - LINEAR ALGEBRA APPL VL - accepted: 15 Oct 2023 PY - 2024 SP - & SN - 0024-3795 UR - https://m2.mtmt.hu/api/publication/34767259 ID - 34767259 AB - We give systematic ways of defining monotone quantum relative entropies and (multi-variate) quantum Rényi divergences starting from a set of monotone quantum relative entropies. Despite its central importance in information theory, only two additive and monotone quantum extensions of the classical relative entropy have been known so far, the Umegaki and the Belavkin-Staszewski relative entropies. Here we give a general procedure to construct monotone and additive quantum relative entropies from a given one with the same properties; in particular, when starting from the Umegaki relative entropy, this gives a new one-parameter family of monotone and additive quantum relative entropies interpolating between the Umegaki and the Belavkin-Staszewski ones on full-rank states. In a different direction, we use a generalization of a classical variational formula to define multi-variate quantum Rényi quantities corresponding to any finite set of quantum relative entropies (Dqx)x∈X and signed probability measure P, as Qb,qP((ρx)x∈X):=supτ≥0{Trτ−∑xP(x)Dqx(τ∥ρx)}. We show that monotone quantum relative entropies define monotone Rényi quantities whenever P is a probability measure. With the proper normalization, the negative logarithm of the above quantity gives a quantum extension of the classical Rényi α-divergence in the 2-variable case (X={0,1}, P(0)=α). We show that if both Dq0 and Dq1 are monotone and additive quantum relative entropies, and at least one of them is strictly larger than the Umegaki relative entropy then the resulting barycentric Rényi divergences are strictly between the log-Euclidean and the maximal Rényi divergences, and hence they are different from any previously studied quantum Rényi divergence. LA - English DB - MTMT ER - TY - JOUR AU - Pollicott, M.A.R.K. AU - Sewell, Benedict Adam TI - An elementary proof that the Rauzy gasket is fractal JF - ERGODIC THEORY AND DYNAMICAL SYSTEMS J2 - ERGOD THEOR DYN SYST PY - 2024 SN - 0143-3857 DO - 10.1017/etds.2023.66 UR - https://m2.mtmt.hu/api/publication/34689502 ID - 34689502 N1 - Published online by Cambridge University Press: 25 September 2023 Correspondence Address: Sewell, B.; Alfréd Rényi Institute, 13-15 Reáltonoda utca, Hungary; email: sewell@renyi.hu Funding details: 833802-Resonances Funding details: Engineering and Physical Sciences Research Council, EPSRC, EP/T001674/1 Funding text 1: The first author is partly supported by ERC-Advanced Grant 833802-Resonances and EPSRC grant EP/T001674/1, and the second by the Alfréd Rényi Young Researcher Fund. AB - We present an elementary proof that the Rauzy gasket has Hausdorff dimension strictly smaller than two. © The Author(s), 2023. Published by Cambridge University Press. LA - English DB - MTMT ER - TY - JOUR AU - Pollicott, M. AU - Sewell, Benedict Adam TI - An infinite interval version of the α-Kakutani equidistribution problem JF - ISRAEL JOURNAL OF MATHEMATICS J2 - ISR J MATH VL - Published: 13 November 2023 PY - 2024 SP - & SN - 0021-2172 DO - 10.1007/s11856-023-2569-6 UR - https://m2.mtmt.hu/api/publication/34689501 ID - 34689501 N1 - Export Date: 27 February 2024 Correspondence Address: Pollicott, M.; Mathematics Institute, United Kingdom; email: masdbl@warwick.ac.uk Funding details: 833802-Resonances Funding details: Engineering and Physical Sciences Research Council, EPSRC, EP/T001674/1 Funding text 1: Partly supported by ERC-Advanced Grant 833802-Resonances and EPSRC grant EP/T001674/1. AB - In this article we extend results of Kakutani, Adler–Flatto, Smilansky and others on the classical α-Kakutani equidistribution result for sequences arising from finite partitions of the interval. In particular, we describe a generalization of the equidistribution result to infinite partitions. In addition, we give discrepancy estimates, extending results of Drmota–Infusino [8]. © 2023, The Author(s). LA - English DB - MTMT ER - TY - JOUR AU - Andrievskii, Vladimir AU - Kroó, András AU - Szabados, József TI - In Memoriam Richard S. Varga October 9, 1928-February 25, 2022 JF - JOURNAL OF APPROXIMATION THEORY J2 - J APPROX THEORY VL - 297 PY - 2024 PG - 26 SN - 0021-9045 DO - 10.1016/j.jat.2023.105971 UR - https://m2.mtmt.hu/api/publication/34588983 ID - 34588983 LA - English DB - MTMT ER - TY - JOUR AU - Kroó, András TI - Lp Bernstein type inequalities for star like Lip α domains JF - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS J2 - J MATH ANAL APPL VL - 532 PY - 2024 IS - 2 PG - 16 SN - 0022-247X DO - 10.1016/j.jmaa.2023.127986 UR - https://m2.mtmt.hu/api/publication/34584881 ID - 34584881 N1 - Export Date: 18 March 2024 Funding details: Hungarian Scientific Research Fund, OTKA, K128922 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFI Funding text 1: Supported by the NKFIH - OTKA Grant K128922. AB - The goal of the present paper is to establish that square root of the Euclidean distance to the boundary is the universal measure suitable for obtaining L-p Bernstein type inequalities on general star like Lip 1 domains. This will be proved for derivatives of any order, every 0 < p < infinity and generalized Jacobi type weights. A converse result will show that the "square root of the Euclidean distance to the boundary" in general is the best possible measure in the vicinity of any vertex of a convex polytope. In addition we will also consider cuspidal Lip alpha, 0 < alpha < 1 graph domains. It turns out that for such cuspidal domains the situation can change dramatically: instead of taking the square root we need to use the (1/alpha - 1/2 )-th power of the Euclidean distance to the boundary when 0 < alpha < 1, and this measure of the distance to the boundary is in general the best possible, as well.(c) 2023 The Author(s). Published by Elsevier Inc. LA - English DB - MTMT ER - TY - JOUR AU - Gselmann, Eszter AU - Kiss, Gergely TI - Polynomial Equations for Additive Functions I: The Inner Parameter Case JF - RESULTS IN MATHEMATICS J2 - RES MATHEM VL - 79 PY - 2024 IS - 2 PG - 37 SN - 1422-6383 DO - 10.1007/s00025-023-02087-y UR - https://m2.mtmt.hu/api/publication/34542247 ID - 34542247 AB - The aim of this sequence of work is to investigate polynomial equations satisfied by additive functions. As a result of this, new characterization theorems for homomorphisms and derivations can be given. More exactly, in this paper the following type of equation is considered \begin{aligned} \sum _{i=1}^{n}f_{i}(x^{p_{i}})g_{i}(x^{q_{i}})= 0 \qquad \left( x\in \mathbb {F}\right) , \end{aligned} ∑ i = 1 n f i ( x p i ) g i ( x q i ) = 0 x ∈ F , where n is a positive integer, \mathbb {F}\subset \mathbb {C} F ⊂ C is a field, f_{i}, g_{i}:\mathbb {F}\rightarrow \mathbb {C} f i , g i : F → C are additive functions and p_i, q_i p i , q i are positive integers for all i=1, \ldots , n i = 1 , … , n . LA - English DB - MTMT ER - TY - JOUR AU - Kiss, Gergely AU - Matolcsi, Dávid AU - Matolcsi, Máté AU - Somlai, Gábor TI - Tiling and weak tiling in (Zp)d JF - Sampling Theory, Signal Processing, and Data Analysis J2 - Sampl. Theory Signal Process. Data Anal. VL - 22 PY - 2024 IS - 1 SN - 2730-5716 DO - 10.1007/s43670-023-00073-7 UR - https://m2.mtmt.hu/api/publication/34429446 ID - 34429446 N1 - Alfréd Rényi Institute of Mathematics, HUN-REN, Reáltanoda u. 13-15, Budapest, 1053, Hungary Eötvös Loránd University, Pázmány Péter sétány 1/C, Budapest, 1111, Hungary Department of Analysis, Institute of Mathematics, Budapest University of Technology and Economics (BME), Müegyetem rkp. 3, Budapest, 1111, Hungary Export Date: 14 December 2023 Correspondence Address: Matolcsi, M.; Department of Analysis, Müegyetem rkp. 3, Hungary; email: matomate@renyi.hu AB - We discuss the relation of tiling, weak tiling and spectral sets in finite abelian groups. In particular, in elementary p -groups (\mathbb {Z}_p)^d ( Z p ) d , we introduce an averaging procedure that leads to a natural object of study: a 4-tuple of functions which can be regarded as a common generalization of tiles and spectral sets. We characterize such 4-tuples for d=1, 2 d = 1 , 2 , and prove some partial results for d=3 d = 3 . LA - English DB - MTMT ER - TY - GEN AU - Gselmann, Eszter AU - Kiss, Gergely TI - Polynomial equations for additive functions II PY - 2024 PG - 29 UR - https://m2.mtmt.hu/api/publication/34155756 ID - 34155756 AB - In this sequence of work we investigate polynomial equations of additive functions. We consider the solutions of equation ∑i=1nfi(xpi)gi(x)qi=0(x∈F), where n is a positive integer, F⊂C is a field, fi,gi:F→C are additive functions and pi,qi are positive integers for all i=1,…,n. Using the theory of decomposable functions we describe the solutions as compositions of higher order derivations and field homomorphisms. In many cases we also give a tight upper bound for the order of the involved derivations. Moreover, we present the full description of the solutions in some important special cases, too. LA - English DB - MTMT ER - TY - JOUR AU - Ambrus, Gergely AU - Csiszárik, Adrián AU - Matolcsi, Máté AU - Varga, Dániel AU - Zsámboki, Pál TI - The density of planar sets avoiding unit distances JF - MATHEMATICAL PROGRAMMING J2 - MATH PROGRAM VL - Published: 06 October 2023 PY - 2024 SN - 0025-5610 DO - 10.1007/s10107-023-02012-9 UR - https://m2.mtmt.hu/api/publication/33834838 ID - 33834838 N1 - Published onlline: 06 October 2023 Department of Geometry, Bolyai Institute, University of Szeged, Aradi vért. tere 1, Szeged, 6720, Hungary HUN-REN Alfréd Rényi Institute of Mathematics, Reáltanoda u. 13-15, Budapest, 1053, Hungary Department of Computer Science, Institute of Mathematics, Eötvös Loránd University, Pázmány Péter sétány 1/C, Budapest, 1117, Hungary Department of Analysis, Institute of Mathematics, Budapest University of Technology and Economics, Műegyetem rkp. 3, Budapest, 1111, Hungary Export Date: 26 October 2023 Correspondence Address: Ambrus, G.; Department of Geometry, Aradi vért. tere 1, Hungary; email: ambrus@renyi.hu AB - By improving upon previous estimates on a problem posed by L. Moser, we prove a conjecture of Erdős that the density of any measurable planar set avoiding unit distances is less than 1/4. Our argument implies the upper bound of 0.2470. LA - English DB - MTMT ER -