@article{MTMT:34767759,
	title = {Special families of piecewise linear iterated function systems},
	url = {https://m2.mtmt.hu/api/publication/34767759},
	author = {Prokaj, Rudolf Dániel and Simon, Károly},
	journal-iso = {DYNAM SYST APPL},
	journal = {DYNAMIC SYSTEMS AND APPLICATIONS},
	volume = {accepted},
	unique-id = {34767759},
	issn = {1056-2176},
	abstract = {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.},
	year = {2024},
	pages = {&}
}

@article{MTMT:34767259,
	title = {Geometric relative entropies and barycentric Rényi divergences},
	url = {https://m2.mtmt.hu/api/publication/34767259},
	author = {Mosonyi, Milán and Bunth, Gergely and Vrana, Péter},
	journal-iso = {LINEAR ALGEBRA APPL},
	journal = {LINEAR ALGEBRA AND ITS APPLICATIONS},
	volume = {accepted: 15 Oct 2023},
	unique-id = {34767259},
	issn = {0024-3795},
	abstract = {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.},
	year = {2024},
	eissn = {1873-1856},
	pages = {&},
	orcid-numbers = {Vrana, Péter/0000-0003-0770-0432}
}

@article{MTMT:34689502,
	title = {An elementary proof that the Rauzy gasket is fractal},
	url = {https://m2.mtmt.hu/api/publication/34689502},
	author = {Pollicott, M.A.R.K. and Sewell, Benedict Adam},
	doi = {10.1017/etds.2023.66},
	journal-iso = {ERGOD THEOR DYN SYST},
	journal = {ERGODIC THEORY AND DYNAMICAL SYSTEMS},
	unique-id = {34689502},
	issn = {0143-3857},
	abstract = {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.},
	keywords = {Hausdorff dimension; projective iterated function systems; Rauzy gasket; self-projective attractors},
	year = {2024},
	eissn = {1469-4417}
}

@article{MTMT:34689501,
	title = {An infinite interval version of the α-Kakutani equidistribution problem},
	url = {https://m2.mtmt.hu/api/publication/34689501},
	author = {Pollicott, M. and Sewell, Benedict Adam},
	doi = {10.1007/s11856-023-2569-6},
	journal-iso = {ISR J MATH},
	journal = {ISRAEL JOURNAL OF MATHEMATICS},
	volume = {Published: 13 November 2023},
	unique-id = {34689501},
	issn = {0021-2172},
	abstract = {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).},
	year = {2024},
	eissn = {1565-8511},
	pages = {&}
}

@article{MTMT:34588983,
	title = {In Memoriam Richard S. Varga October 9, 1928-February 25, 2022},
	url = {https://m2.mtmt.hu/api/publication/34588983},
	author = {Andrievskii, Vladimir and Kroó, András and Szabados, József},
	doi = {10.1016/j.jat.2023.105971},
	journal-iso = {J APPROX THEORY},
	journal = {JOURNAL OF APPROXIMATION THEORY},
	volume = {297},
	unique-id = {34588983},
	issn = {0021-9045},
	year = {2024},
	eissn = {1096-0430}
}

@article{MTMT:34584881,
	title = {L<sub>p</sub> Bernstein type inequalities for star like Lip α domains},
	url = {https://m2.mtmt.hu/api/publication/34584881},
	author = {Kroó, András},
	doi = {10.1016/j.jmaa.2023.127986},
	journal-iso = {J MATH ANAL APPL},
	journal = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS},
	volume = {532},
	unique-id = {34584881},
	issn = {0022-247X},
	abstract = {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.},
	keywords = {Multivariate Polynomials; Bernstein-Markov inequality; Cuspidal sets; L- p norm},
	year = {2024},
	eissn = {1096-0813}
}

@article{MTMT:34542247,
	title = {Polynomial Equations for Additive Functions I: The Inner Parameter Case},
	url = {https://m2.mtmt.hu/api/publication/34542247},
	author = {Gselmann, Eszter and Kiss, Gergely},
	doi = {10.1007/s00025-023-02087-y},
	journal-iso = {RES MATHEM},
	journal = {RESULTS IN MATHEMATICS},
	volume = {79},
	unique-id = {34542247},
	issn = {1422-6383},
	abstract = {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 .},
	keywords = {decomposable function},
	year = {2024},
	eissn = {1420-9012},
	orcid-numbers = {Gselmann, Eszter/0000-0002-1708-2570}
}

@article{MTMT:34429446,
	title = {Tiling and weak tiling in (Zp)d},
	url = {https://m2.mtmt.hu/api/publication/34429446},
	author = {Kiss, Gergely and Matolcsi, Dávid and Matolcsi, Máté and Somlai, Gábor},
	doi = {10.1007/s43670-023-00073-7},
	journal-iso = {Sampl. Theory Signal Process. Data Anal.},
	journal = {Sampling Theory, Signal Processing, and Data Analysis},
	volume = {22},
	unique-id = {34429446},
	issn = {2730-5716},
	abstract = {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 .},
	year = {2024},
	eissn = {2730-5724},
	orcid-numbers = {Matolcsi, Máté/0000-0003-4889-697X}
}

@misc{MTMT:34155756,
	title = {Polynomial equations for additive functions II},
	url = {https://m2.mtmt.hu/api/publication/34155756},
	author = {Gselmann, Eszter and Kiss, Gergely},
	unique-id = {34155756},
	abstract = {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.},
	year = {2024},
	orcid-numbers = {Gselmann, Eszter/0000-0002-1708-2570}
}

@article{MTMT:33834838,
	title = {The density of planar sets avoiding unit distances},
	url = {https://m2.mtmt.hu/api/publication/33834838},
	author = {Ambrus, Gergely and Csiszárik, Adrián and Matolcsi, Máté and Varga, Dániel and Zsámboki, Pál},
	doi = {10.1007/s10107-023-02012-9},
	journal-iso = {MATH PROGRAM},
	journal = {MATHEMATICAL PROGRAMMING},
	volume = {Published: 06 October 2023},
	unique-id = {33834838},
	issn = {0025-5610},
	abstract = {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.},
	year = {2024},
	eissn = {1436-4646},
	orcid-numbers = {Ambrus, Gergely/0000-0003-1246-6601; Matolcsi, Máté/0000-0003-4889-697X}
}