Mateusz Kwaśnicki

activity

20092026

most citedBoundary Harnack inequality for Markov processes with jumps

75 citations · 258 across the 15 of their papers we have counts for

collaborators

24 papers

math-ph2026

Dynamics of low energy wave packets in the one-dimensional quantum Heisenberg ferromagnet

Mateusz Kwaśnicki, Marcin Napiórkowski, Sören Petrat +1

Spin wave theory plays a central role in the analysis of low-energy properties of the quantum ferromagnetic Heisenberg model. In this work, we present a first step towards a rigoro…

math.PR2026

Large time behavior of Lévy processes and their nonlocal Schrödinger semigroups

Mateusz Kwaśnicki, Phanuel Mariano, Hugo Panzo +1

We study the large time asymptotics of the Feynman-Kac semigroups of the symmetric Lévy process on unbounded open sets. Our main result proves the exact exponential asymptotic deca…

math.PR2026

Bell-shaped functions are Poisson kernels

Mateusz Kwaśnicki

In a recent paper [Kwaśnicki, Poisson kernels on the half-plane are bell-shaped, Bull. London Math. Soc. 58 (2026), no. e70303], the author proved that Poisson kernels for a class…

math.SP2026

Generalised eigenvector expansion of infinite Toeplitz matrices with absolutely/completely monotone entries

Mateusz Kwaśnicki, Jacek Wszoła

We study the spectral theory of infinite Toeplitz matrices $T = (a_{k - l})$ under the assumption that $(a_{k})$ and $(a_{- k})$ are completely monotone sequences. We derive expressio…

math.PR2019

Boundary traces of shift-invariant diffusions in half-plane

Mateusz Kwaśnicki

We study boundary traces of shift-invariant diffusions: two-dimensional diffusions in the upper half-plane $R \times [0, \infty)$ (or in $R \times [0, R)$ ) invari…

math.PR2019

Characterisation of the class of bell-shaped functions

Mateusz Kwaśnicki, Thomas Simon

A non-negative function $f$ is said to be 'bell-shaped' if $f$ tends to zero at $\pm \infty$ and the $n$ -th derivative of $f$ changes its sign $n$ times for every $n = 0, 1, 2, \ld…

math.AP2019

Harmonic extension technique for non-symmetric operators with completely monotone kernels

Mateusz Kwaśnicki

We identify a class of non-local integro-differential operators $K$ in $R$ with Dirichlet-to-Neumann maps in the half-plane $R \times (0, \infty)$ for appropriate…

math.PR2019

Random walks are determined by their trace on the positive half-line

Mateusz Kwaśnicki

We prove that the law of a random walk $X_{n}$ is determined by the one-dimensional distributions of $max (X_{n}, 0)$ for $n = 1, 2, \dots$ , as conjectured recently by Loïc Chaumont a…

math.PR2018

Fluctuation theory for Lévy processes with completely monotone jumps

Mateusz Kwaśnicki

We study the Wiener-Hopf factorization for Lévy processes $X_{t}$ with completely monotone jumps. Extending previous results of L.C.G. Rogers, we prove that the space-time Wiener-Hop…

math.CA2017★ 13 cited

On the $l^{p}$ -norm of the discrete Hilbert transform

Rodrigo Bañuelos, Mateusz Kwaśnicki

Using a representation of the discrete Hilbert transform in terms of martingales arising from Doob $h$ -processes, we prove that its $l^{p}$ -norm, $1 < p < \infty$ , is bounded above by th…

math.CA2017

A new class of bell-shaped functions

Mateusz Kwaśnicki

We provide a large class of functions $f$ that are bell-shaped: the $n$ -th derivative of $f$ changes its sign exactly $n$ times. This class is described by means of Stieltjes-type…

math.PR2016★ 23 cited

Potential kernels, probabilities of hitting a ball, harmonic functions and the boundary Harnack inequality for unimodal Lévy processes

Tomasz Grzywny, Mateusz Kwaśnicki

In the first part of this article, we prove two-sided estimates of hitting probabilities of balls, the potential kernel and the Green function for a ball for general isotropic unim…

math.SP2016

Pólya's conjecture fails for the fractional Laplacian

Mateusz Kwaśnicki, Richard S. Laugesen, Bartłomiej A. Siudeja

The analogue of Pólya's conjecture is shown to fail for the fractional Laplacian (-Delta)^{alpha/2} on an interval in 1-dimension, whenever 0 < alpha < 2. The failure is total: eve…

math.PR2015

Contractivity and ground state domination properties for non-local Schrödinger operators

Kamil Kaleta, Mateusz Kwaśnicki, József Lőrinczi

We study supercontractivity and hypercontractivity of Markov semigroups obtained via ground state transformation of non-local Schrödinger operators based on generators of symmetric…

math.SP2015★ 3 cited

Asymptotic estimate of eigenvalues of pseudo-differential operators in an interval

Kamil Kaleta, Mateusz Kwaśnicki, Jacek Małecki

We prove a two-term Weyl-type asymptotic law, with error term O(1/n), for the eigenvalues of the operator psi(-Delta) in an interval, with zero exterior condition, for complete Ber…

math.PR2014★ 9 cited

Hitting times of points for symmetric Lévy processes with completely monotone jumps

Tomasz Juszczyszyn, Mateusz Kwaśnicki

Small-space and large-time estimates and asymptotic expansion of the distribution function and (the derivatives of) the density function of hitting times of points for symmetric Lé…

math.PR2014★ 3 cited

New families of subordinators with explicit transition probability semigroup

James Burridge, Mateusz Kwaśnicki, Alexey Kuznetsov +1

There exist only a few known examples of subordinators for which the transition probability density can be computed explicitly along side an expression for its Lévy measure and Lap…

math.CV2013★ 6 cited

Rogers functions and fluctuation theory

Mateusz Kwaśnicki

Extending earlier work by Rogers, Wiener-Hopf factorisation is studied for a class of functions closely related to Nevanlinna-Pick functions and complete Bernstein functions. The n…

math.PR2012★ 75 cited

Boundary Harnack inequality for Markov processes with jumps

Krzysztof Bogdan, Takashi Kumagai, Mateusz Kwaśnicki

We prove a boundary Harnack inequality for jump-type Markov processes on metric measure state spaces, under comparability estimates of the jump kernel and Urysohn-type property of…

math.AP2011★ 10 cited

On high spots of the fundamental sloshing eigenfunctions in axially symmetric domains

Tadeusz Kulczycki, Mateusz Kwaśnicki

We investigate the classical eigenvalue problem that arises in hydrodynamics and is referred to as the sloshing problem. It describes free liquid oscillations in a liquid container…

math.PR2011★ 47 cited

Suprema of Lévy processes

Mateusz Kwaśnicki, Jacek Małecki, Michał Ryznar

In this paper we study the supremum functional $M_{t} = sup_{0 \leq s \leq t} X_{s}$ , where $X_{t}$ , $t \geq 0$ , is a one-dimensional Lévy process. Under very mild assumptions we provide a simple…

math.SP2010

Eigenvalues of the fractional Laplace operator in the interval

Mateusz Kwaśnicki

Two-term Weyl-type asymptotic law for the eigenvalues of one-dimensional fractional Laplace operator (-d^2/dx^2)^(alpha/2) (0 < alpha < 2) in the interval (-1,1) is given: the n-th…

math.SP2009★ 69 cited

Spectral properties of the Cauchy process

Tadeusz Kulczycki, Mateusz Kwaśnicki, Jacek Małecki +1

We study the spectral properties of the transition semigroup of the killed one-dimensional Cauchy process on the half-line (0,infty) and the interval (-1,1). This process is relate…

math.PR2009

Boundary Harnack Inequality for alpha-harmonic functions on the Sierpiński triangle

Kamil Kaleta, Mateusz Kwaśnicki

We prove an uniform boundary Harnack inequality for nonnegative functions harmonic with respect to $α$ -stable process on the Sierpi{ń}ski triangle, where $α \in (0, 1)$ . Our result…

Dynamics of low energy wave packets in the one-dimensional quantum Heisenberg ferromagnet

Large time behavior of Lévy processes and their nonlocal Schrödinger semigroups

Bell-shaped functions are Poisson kernels

Generalised eigenvector expansion of infinite Toeplitz matrices with absolutely/completely monotone entries

Boundary traces of shift-invariant diffusions in half-plane

Characterisation of the class of bell-shaped functions

Harmonic extension technique for non-symmetric operators with completely monotone kernels

Random walks are determined by their trace on the positive half-line

Fluctuation theory for Lévy processes with completely monotone jumps

On the lp-norm of the discrete Hilbert transform

A new class of bell-shaped functions

Potential kernels, probabilities of hitting a ball, harmonic functions and the boundary Harnack inequality for unimodal Lévy processes

Pólya's conjecture fails for the fractional Laplacian

Contractivity and ground state domination properties for non-local Schrödinger operators

Asymptotic estimate of eigenvalues of pseudo-differential operators in an interval

Hitting times of points for symmetric Lévy processes with completely monotone jumps

New families of subordinators with explicit transition probability semigroup

Rogers functions and fluctuation theory

Boundary Harnack inequality for Markov processes with jumps

On high spots of the fundamental sloshing eigenfunctions in axially symmetric domains

Suprema of Lévy processes

Eigenvalues of the fractional Laplace operator in the interval

Spectral properties of the Cauchy process

Boundary Harnack Inequality for alpha-harmonic functions on the Sierpiński triangle

On the $l^{p}$ -norm of the discrete Hilbert transform