75 citations · 258 across the 15 of their papers we have counts for
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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 under the assumption that and are completely monotone sequences. We derive expressio…
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…
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…
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…
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…