139 citations · 575 across the 36 of their papers we have counts for
6 papers · 1 filter
A short proof of duality relations for hypergeometric functions
Runhuan Feng, Alexey Kuznetsov, Fenghao Yang
Identities involving finite sums of products of hypergeometric functions and their duals have been studied since 1930s. Recently Beukers and Jouhet have used an algebraic approach…
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…
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…
Using -calculus to study factorization of a certain Vandermonde matrix
Alexey Kuznetsov
We use tools from -calculus to study decomposition of the Vandermonde matrix with coefficients . We prove that the matrix is given as a product…
Explicit Hermite-type eigenvectors of the discrete Fourier transform
Alexey Kuznetsov
The search for a canonical set of eigenvectors of the discrete Fourier transform has been ongoing for more than three decades. The goal is to find an orthogonal basis of eigenvecto…