HUN-REN Alfréd Rényi Institute of Mathematics

output

19942026

most citedBrownian distance covariance

857 citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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48 papers · 1 filter

math.CA2022★ 5 cited

Spectral sets and weak tiling

Mihail N. Kolountzakis, Nir Lev, Máté Matolcsi

A set $Ω \subset R^{d}$ is said to be spectral if the space $L^{2} (Ω)$ admits an orthogonal basis of exponential functions. Fuglede (1974) conjectured that $Ω$ is spectral if a…

math.CA2022★ 3 cited

Dingle's final main rule, Berry's transition, and Howls' conjecture

Gergő Nemes

The Stokes phenomenon is the apparent discontinuous change in the form of the asymptotic expansion of a function across certain rays in the complex plane, known as Stokes lines, as…

math.CA2021★ 1 cited

Generic Hölder level sets and fractal conductivity

Zoltán Buczolich, Balázs Maga, Gáspár Vértesy

Hausdorff dimensions of level sets of generic continuous functions defined on fractals can give information about the "thickness/narrow cross-sections'' of a "network" correspondin…

math.CA2021★ 2 cited

Generic Hölder level sets on Fractals

Zoltán Buczolich, Balázs Maga, Gáspár Vértesy

Hausdorff dimensions of level sets of generic continuous functions defined on fractals were considered in two papers by R. Balka, Z. Buczolich and M. Elekes. In those papers the to…

math.CA2021

Strong one-sided density without uniform density

Zoltán Buczolich, Bruce Hanson, Balázs Maga +1

In this paper we give an example of a closed, strongly one-sided dense set which is not of uniform density type. We also show that there is a set of uniform density type which is n…

math.CA2020★ 20 cited

Fuglede's conjecture holds for cyclic groups of order $pq r s$

Gergely Kiss, Romanos Diogenes Malikiosis, Gábor Somlai +1

The tile-spectral direction of the discrete Fuglede-conjecture is well-known for cyclic groups of square-free order, initiated by Laba and Meyerowitz, but the spectral-tile directi…

math.CA2020

Singularity of maps of several variables and a problem of Mycielski concerning prevalent homeomorphisms

Richárd Balka, Márton Elekes, Viktor Kiss +1

S. Banach pointed out that the graph of the generic (in the sense of Baire category) element of $Homeo ([0, 1])$ has length $2$ . J. Mycielski asked if the measure theoretic du…

math.CA2020★ 2 cited

Stability of the Prekopa-Leindler inequality for log-concave functions

Karoly J. Boroczky, Apratim De

Stability version of the Prekopa-Leindler inequality for log-concave functions on the n-dimensional Euclidean space is established.

math.CA2020★ 13 cited

On the Borel summability of WKB solutions of certain Schrödinger-type differential equations

Gergő Nemes

A class of Schrödinger-type second-order linear differential equations with a large parameter $u$ is considered. Analytic solutions of this type of equations can be described via (…

math.CA2019★ 96 cited

The Fuglede conjecture for convex domains is true in all dimensions

Nir Lev, Máté Matolcsi

A set $Ω \subset R^{d}$ is said to be spectral if the space $L^{2} (Ω)$ has an orthogonal basis of exponential functions. A conjecture due to Fuglede (1974) stated that $Ω$ is a…

math.CA2018★ 22 cited

On the discrete Fuglede and Pompeiu problems

Gergely Kiss, Romanos Diogenes Malikiosis, Gábor Somlai +1

We investigate the discrete Fuglede's conjecture and Pompeiu problem on finite abelian groups and develop a strong connection between the two problems. We give a geometric conditio…

math.CA2017★ 66 cited

The $L_{p}$ -Minkowski problem for $- n < p < 1$

Gabriele Bianchi, Károly J. Böröczky, Andrea Colesanti +1

Chou and Wang's existence result for the $L_{p}$ -Minkowski problem on $S^{n - 1}$ for $p \in (- n, 1)$ and an absolutely continuous measure $μ$ is discussed and extended to more…

math.CA2015★ 13 cited

A potential theoretic minimax problem on the torus

Bálint Farkas, Béla Nagy, Szilárd Gy. Révész

We investigate an extension of an equilibrium-type result, conjectured by Ambrus, Ball and Erdélyi, and proved recently by Hardin, Kendall and Saff. These results were formulated o…

math.CA2013★ 12 cited

A family of nonlinear difference equations: existence, uniqueness, and asymptotic behavior of positive solutions

Saud M. Alsulami, Paul Nevai, József Szabados +1

We study solutions $(x_{n})_{n \in N}$ of nonhomogeneous nonlinear second order difference equations of the type $\ell_n = x_n ( σ_{n,1} x_{n+1} + σ_{n,0} x_n + σ_{n,-1} x_{…

math.CA2013★ 9 cited

Bruckner--Garg-type results with respect to Haar null sets in $C [0, 1]$

Richárd Balka, Udayan B. Darji, Márton Elekes

A set $A \subset C [0, 1]$ is \emph{shy} or \emph{Haar null } (in the sense of Christensen) if there exists a Borel set $B \subset C [0, 1]$ and a Borel probability m…

math.CA2012

Answer to a question of Kolmogorov

Richárd Balka, Márton Elekes, András Máthé

More than 80 years ago Kolmogorov asked the following question. Let $E \subseteq R^{2}$ be a measurable set with $λ^{2} (E) < \infty$ , where $λ^{2}$ denotes the two-dimensional…

math.CA2012★ 1 cited

Dimension and measure for generic continuous images

Richárd Balka, Ábel Farkas, Jonathan M. Fraser +1

We consider the Banach space consisting of continuous functions from an arbitrary uncountable compact metric space, $X$ , into $R^{n}$ . The key question is `what is the gener…

math.CA2011

Hausdorff measures of different dimensions are isomorphic under the Continuum Hypothesis

Márton Elekes

We show that the Continuum Hypothesis implies that for every $0 < d_{1} \leq d_{2} < n$ the measure spaces $(\RR^n,\iM_{\iH^{d_1}},\iH^{d_1})$ and $(\RR^n,\iM_{\iH^{d_2}},\iH^{d_2})$ are is…

math.CA2011

Borel sets which are null or non- $σ$ -finite for every translation invariant measure

Márton Elekes, Tamás Keleti

We show that the set of Liouville numbers is either null or non- $σ$ -finite with respect to every translation invariant Borel measure on $\RR$, in particular, with respect to every…

math.CA2011

The structure of rigid functions

Richárd Balka, Márton Elekes

A function $f:\RR \to \RR$ is called \emph{vertically rigid} if $g r a p h (c f)$ is isometric to $g r a p h (f)$ for all $c \neq = 0$ . We prove Janković's conjecture by showing that a continu…

math.CA2011

Continuous horizontally rigid functions of two variables are affine

Richárd Balka, Márton Elekes

Cain, Clark and Rose defined a function $f\colon \RR^n \to \RR$ to be \emph{vertically rigid} if $\graph(cf)$ is isometric to $\graph (f)$ for every $c \neq = 0$ . It is \emph{horizon…

math.CA2011

A cardinal number connected to the solvability of systems of difference equations in a given function class

Márton Elekes, Miklós Laczkovich

Let $R^{R}$ denote the set of real valued functions defined on the real line. A map $D : R^{R} \to R^{R}$ is a {\it difference operator}, if there are real numbers $a_i, b_i \ (i=1,…

math.CA2011

Can we assign the Borel hulls in a monotone way?

Márton Elekes, András Máthé

A \emph{hull} of $A \subset [0, 1]$ is a set $H$ containing $A$ such that $λ^{*} (H) = λ^{*} (A)$ . We investigate all four versions of the following problem. Does there exist a monotone (wr…

math.CA2011

Reconstructing geometric objects from the measures of their intersections with test sets

Márton Elekes, Tamás Keleti, András Máthé

Let us say that an element of a given family $\A$ of subsets of $R^{d}$ can be reconstructed using $n$ test sets if there exist $T_{1}, ..., T_{n} \subset R^{d}$ such that whenever $A,B\in…

Spectral sets and weak tiling

Dingle's final main rule, Berry's transition, and Howls' conjecture

Generic Hölder level sets and fractal conductivity

Generic Hölder level sets on Fractals

Strong one-sided density without uniform density

Fuglede's conjecture holds for cyclic groups of order pqrs

Singularity of maps of several variables and a problem of Mycielski concerning prevalent homeomorphisms

Stability of the Prekopa-Leindler inequality for log-concave functions

On the Borel summability of WKB solutions of certain Schrödinger-type differential equations

The Fuglede conjecture for convex domains is true in all dimensions

On the discrete Fuglede and Pompeiu problems

The Lp​-Minkowski problem for −n<p<1

A potential theoretic minimax problem on the torus

A family of nonlinear difference equations: existence, uniqueness, and asymptotic behavior of positive solutions

Bruckner--Garg-type results with respect to Haar null sets in C[0,1]

Answer to a question of Kolmogorov

Dimension and measure for generic continuous images

Hausdorff measures of different dimensions are isomorphic under the Continuum Hypothesis

Borel sets which are null or non-σ-finite for every translation invariant measure

The structure of rigid functions

Continuous horizontally rigid functions of two variables are affine

A cardinal number connected to the solvability of systems of difference equations in a given function class

Can we assign the Borel hulls in a monotone way?

Reconstructing geometric objects from the measures of their intersections with test sets

Fuglede's conjecture holds for cyclic groups of order $pq r s$

The $L_{p}$ -Minkowski problem for $- n < p < 1$

Bruckner--Garg-type results with respect to Haar null sets in $C [0, 1]$

Borel sets which are null or non- $σ$ -finite for every translation invariant measure