Jacek Wszoła

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20222026

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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…