7 papers
Extension technique for complete Bernstein functions of the Laplace operator
Mateusz Kwaśnicki, Jacek Mucha
We discuss representation of certain functions of the Laplace operator as Dirichlet-to-Neumann maps for appropriate elliptic operators in half-space. A classical result identif…
Minimal Hermite-type eigenbasis of the discrete Fourier transform
Alexey Kuznetsov, Mateusz Kwaśnicki
There exist many ways to build an orthonormal basis of , consisting of the eigenvectors of the discrete Fourier transform (DFT). In this paper we show that there is o…
Fractional Laplace operator and Meijer G-function
Bartłomiej Dyda, Alexey Kuznetsov, Mateusz Kwaśnicki
We significantly expand the number of functions whose image under the fractional Laplace operator can be computed explicitly. In particular, we show that the fractional Laplace ope…
Martin kernels for Markov processes with jumps
Tomasz Juszczyszyn, Mateusz Kwaśnicki
We prove existence of boundary limits of ratios of positive harmonic functions for a wide class of Markov processes with jumps and irregular domains, in the context of general metr…
Eigenvalues of the fractional Laplace operator in the unit ball
Bartłomiej Dyda, Alexey Kuznetsov, Mateusz Kwaśnicki
We describe a highly efficient numerical scheme for finding two-sided bounds for the eigenvalues of the fractional Laplace operator (-Delta)^{alpha/2} in the unit ball D in R^d, wi…
Spectral analysis of stable processes on the positive half-line
Alexey Kuznetsov, Mateusz Kwasnicki
We study the spectral expansion of the semigroup of a general stable process killed on the first exit from the positive half-line. Starting with the Wiener-Hopf factorization we ob…