Zobrazeno 1 - 10
of 279
pro vyhledávání: '"P. Kwaśnicki"'
We revisit a Harnack inequality for antisymmetric functions that has been recently established for the fractional Laplacian and we extend it to more general nonlocal elliptic operators. The new approach to deal with these problems that we propose in
Externí odkaz:
http://arxiv.org/abs/2411.11272
Autor:
Kwaśnicki, Mateusz
Consider a path of the reflected Brownian motion in the half-plane $\{y \ge 0\}$, and erase its part contained in the interior $\{y > 0\}$. What is left is, in an appropriate sense, a path of a jump-type stochastic process on the line $\{y = 0\}$ --
Externí odkaz:
http://arxiv.org/abs/2409.19118
Autor:
Kwaśnicki, Mateusz, Wszoła, Jacek
A nonnegative real function f is bell-shaped if it converges to zero at plus and minus infinity and the nth derivative of f changes sign n times for every n = 0, 1, 2, ... Similarly, a two-sided nonnegative sequence a(k) is bell-shaped if it converge
Externí odkaz:
http://arxiv.org/abs/2404.11274
Autor:
Gutowski, Michał, Kwaśnicki, Mateusz
Sobolev-Bregman forms, or $p$-forms, describe Markovian semigroups on $L^p$, and they reduce to Dirichlet forms when $p = 2$. We prove a variant of the Beurling-Deny formula for Sobolev-Bregman forms which correspond to an arbitrary regular Dirichlet
Externí odkaz:
http://arxiv.org/abs/2312.10824
Autor:
Kwaśnicki, Mateusz
We give a short proof of simplicity of the eigenvalues of the fractional Laplace operator in an interval, a result shown recently by Fall, Ghimenti, Micheletti and Pistoia [Calc. Var. Partial Differ. Equ. 62 (2023), #233].
Comment: 1 page
Comment: 1 page
Externí odkaz:
http://arxiv.org/abs/2311.00713
Autor:
Kwaśnicki, Mateusz
We prove a non-extinction result for Fleming-Viot-type systems of two particles with dynamics described by an arbitrary symmetric Hunt process under the assumption that the reference measure is finite. Additionally, we describe an invariant measure f
Externí odkaz:
http://arxiv.org/abs/2307.04143
Autor:
Grzywny, Tomasz, Kwaśnicki, Mateusz
Let $L$ be a L\'evy operator. A function $h$ is said to be harmonic with respect to $L$ if $L h = 0$ in an appropriate sense. We prove Liouville's theorem for positive functions harmonic with respect to a general L\'evy operator $L$: such functions a
Externí odkaz:
http://arxiv.org/abs/2301.08540
Autor:
Kwaśnicki, Mateusz
We study spectral-theoretic properties of non-self-adjoint operators arising in the study of one-dimensional L\'evy processes with completely monotone jumps with a one-sided barrier. With no further assumptions, we provide an integral expression for
Externí odkaz:
http://arxiv.org/abs/2212.11390
We study axiomatic foundations for different classes of constant-function automated market makers (CFMMs). We focus particularly on separability and on different invariance properties under scaling. Our main results are an axiomatic characterization
Externí odkaz:
http://arxiv.org/abs/2210.00048
Autor:
Bañuelos, Rodrigo, Kwaśnicki, Mateusz
The long-standing conjecture that for $p \in (1, \infty)$ the $\ell^p(\mathbb Z)$ norm of the Riesz--Titchmarsh discrete Hilbert transform is the same as the $L^p(\mathbb R)$ norm of the classical Hilbert transform, is verified when $p = 2 n$ or $\fr
Externí odkaz:
http://arxiv.org/abs/2210.00027