Jacek Wszoła

activity

20222026

collaborators

8 papers

math.SP2026

Eigenvalues of Hermitian Toeplitz matrices with Fisher--Hartwig symbols

Jacek Wszoła

We investigate the eigenvalues of Hermitian Toeplitz matrices generated by the symmetric Fisher-Hartwig symbol $a^(z) = (1 - z)^{α /2} (1 - z^{- 1})^{α /2}$ for $α \in (0, 2)$ . Using Dir…

math.SP2026

Dirichlet--Neumann bracketing for nonlocal operators

Mateusz Kwaśnicki, Jacek Wszoła

We establish Dirichlet--Neumann bracketing for the Dirichlet eigenvalues of $ψ (- Δ)$ on bounded Lipschitz domains, where $ψ$ is an arbitrary complete Bernstein function. The eigenva…

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…

q-fin.PR2025

Design and valuation of multi-region CoCoCat bonds

Jacek Wszoła, Krzysztof Burnecki, Marek Teuerle +1

This paper introduces a novel multidimensional insurance-linked instrument: a contingent convertible bond (CoCoCat bond) whose conversion trigger is activated by predefined natural…

math.PR2025

First passage locations for two-dimensional lattice random walks and the bell-shape

Jacek Wszoła

Let $(X_{n}, Y_{n})$ be a two-dimensional diagonal random walk on the lattice $Z^{2}$ , with transition probabilities depending only on the position of $Y_{n}$ . In this paper, we s…

math.CA2024

Two-sided bell-shaped sequences

Mateusz Kwaśnicki, Jacek Wszoła

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, ... Similarl…

math.AP2023

On the interior Bernoulli free boundary problem for the fractional Laplacian on an interval

Tadeusz Kulczycki, Jacek Wszoła

We study the structure of solutions of the interior Bernoulli free boundary problem for $(- Δ)^{α /2}$ on an interval $D$ with parameter $λ > 0$ . In particular, we show that there exi…

math.CA2022

Bell-shaped sequences

Mateusz Kwaśnicki, Jacek Wszoła

A nonnegative real function $f$ is said to be bell-shaped if it converges to zero at $\pm \infty$ and the $n$ th derivative of $f$ changes sign $n$ times for every $n = 0, 1, 2, \ldo…