Related papers: Discrete Lebedev-Skalskaya transforms
Rubin's generalized Minkowski--Funk transforms $M_t^\alpha$ on the sphere $\mathbb{S}^n$ give rise, for irrational radii $t=\cos(\beta\pi)$, to a small denominator problem governed by the asymptotic behavior of their spectral multipliers.…
Consider the Plancherel decomposition of the tensor product of a highest weight and a lowest weight unitary representations of $SL_2$. We construct explicitly the action of the Lie algebra $sl_2 + sl_2$ in the direct integral of Hilbert…
We develop a potential-theoretic and functional framework for the fractional--logarithmic Laplacian $(-\Delta)^{s+\ln}$ and its inhomogeneous counterpart $(\lambda I-\Delta)^{s+\ln}$ with $\lambda>1$. Their inverses yield logarithmic…
Motivated by problems in control theory concerning decay rates for the damped wave equation $$w_{tt}(x,t) + \gamma(x) w_t(x,t) + (-\Delta + 1)^{s/2} w(x,t) = 0,$$ we consider an analogue of the classical Paneah-Logvinenko-Sereda theorem for…
Spherical Bessel functions appear commonly in many areas of physics wherein there is both translation and rotation invariance, and often integrals over products of several arise. Thus, analytic evaluation of such integrals with different…
We derive a stronger uniqueness result if a function with compact support and its truncated Hilbert transform are known on the same interval by using the Sokhotski-Plemelj formulas. To find a function from its truncated Hilbert transform,…
This paper investigates functional inequalities involving Besov spaces and functions of bounded variation, when the underlying metric measure space displays different local and global structures. Particular focus is put on the $L^1$ theory…
Bialkowski, Erdmann and Skowronski classified those indecomposable self-injective algebras for which the Nakayama shift of every (non-projective) simple module is isomorphic to its third syzygy. It turned out that these are precisely the…
For a given bounded Lipschitz set $\Omega$, we consider a Steklov--type eigenvalue problem for the Laplacian operator whose solutions provide extremal functions for the compact embedding $H^1(\Omega)\hookrightarrow L^2(\partial \Omega)$. We…
An inverse problem in spectroscopy is considered. The objective is to restore the discrete spectrum from observed spectrum data, taking into account the spectrometer's line spread function. The problem is reduced to solution of a system of…
An irreducible module for the parafermion vertex operator algebra $K(\mathfrak{sl}_2,k)$ is said to be of $\sigma$-type if an automorphism of the fusion algebra of $K(\mathfrak{sl}_2,k)$ of order $k$ is trivial on it. For any integer $k \ge…
In this paper, we introduce a family of integral transforms, denoted by \(\mathcal{O}_{\alpha}\), and constructed via kernel fusion of the fractional Fourier transform (FRFT) with angle \(\alpha \notin \pi \mathbb{Z}\). We demonstrate that…
It is known that Struve function $\mathbf H_\nu$ and modified Struve function $\mathbf L_\nu$ are closely connected to Bessel function of the first kind $J_\nu$ and to modified Bessel function of the first kind $I_\nu$ and possess…
The modified Mellin transform ${\cal Z}_k(s) = \int_1^\infty |\zeta({1\over2}+ix|^{2k}x^{-s}{\rm d} x$ ($k\ge1$ is a fixed integer, $s = \sigma + it$) is used to obtain estimates for $$…
We obtain a family of matrix integrals which decompose to a product of Gamma-functions (they have some relations with S.G.Gindikin 'Beta', but generally speaking essentially differ from it). We obtain Plancherel formula for Berezin…
We present a straightforward discretization of the Bessel functions $J_n(x)$ to discrete counterparts $B^{(N)}_n(x_m)$, of $N$ integer orders $n$ on $N$ integer points $x_m \equiv m$, that we call discrete Bessel functions. These are built…
Closed-form evaluations of certain integrals of $J_{0}(\xi)$, the Bessel function of the first kind, have been crucial in the studies on the electromagnetic field of alternating current in a circuit with two groundings, as can be seen from…
Herein we propose a complex form of a genuine Bernstein-Durrmeyer type operators depending on a non-negative real parameter $\alpha.$ We present the quantitative upper bound, Voronovskaja type result and exact order of approximation for…
We study the simple Bershadsky-Polyakov algebra $\mathcal W_k = \mathcal{W}_k(sl_3,f_{\theta})$ at positive integer levels and classify their irreducible modules. In this way we confirm the conjecture from arXiv:1910.13781. Next, we study…
We consider the transformation $\ev$ which associates to any element in a K-algebra A a function on the the set of its K-points. This is the analogue of the fundamental Gelfand transform. Both $\ev$ and its dual $\ev^*$ are the maps from a…