相关论文: Spectral calculations in rings
An integrable polygon is one whose interior angles are fractions of $\pi$; that is to say of the form $\frac \pi n$ for positive integers $n$. We consider the Laplace spectrum on these polygons with the Dirichlet and Neumann boundary…
The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental importance in the theoretical underpinning of kernel methods in…
In the article [11] of L. Kunyansky a symmetric integral identity for Bessel functions of the first and second kind was proved in order to obtain an explicit inversion formula for the spherical mean transform where our data is given on the…
We consider hilbert spaces of holomorphic functions in Cartan domains (in particular in ball and polydisk) and operator of restriction of holomorphic function to a submanifold in Shilov boundary. We discuss conditions when this operator…
We construct spectral zeta functions for the Dirac operator on metric graphs. We start with the case of a rose graph, a graph with a single vertex where every edge is a loop. The technique is then developed to cover any finite graph with…
We find kernel functions of the $q$-Heun equation and its variants. We apply them to obtain $q$-integral transformations of solutions to the $q$-Heun equation and its variants. We discuss special solutions of the $q$-Heun equation from the…
We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring…
A generic method to construct zero-difference functions (ZDFs) on algebraic rings is proposed in this paper. Then this method is used over some rings $\mathbb{Z}_{p^k}$, where $p$ is a prime number and $k\ge 2$ is a positive integer, and…
We study in this work an integral formulation for the radiative transfer equation (RTE) in anisotropic media with truncated approximation to the scattering phase function. The integral formulation consists of a coupled system of integral…
Alternative expressions for calculating the oblate spheroidal radial functions of both kinds R1ml and R2ml are shown to provide accurate values over very large parameter ranges using 64 bit arithmetic, even where the traditional expressions…
We show that the two integrals in the Riemann-Siegel integral formula can be transformed into integral representations that contain the parabolic cylinder function $U(a,z)$ as kernel function.
We construct some explicit formulas of rational maps and transcendental meromorphic functions having Herman rings of period strictly larger than one. This gives an answer to a question raised by Shishikura in the 1980s. Moreover, the…
We study the question of when a ring can be realized as a direct summand of a regular ring by examining the case of homogeneous coordinate rings. We present very strong obstacles to expressing a graded ring with isolated singularity as a…
We describe an effective method for computing the topological degree of continuous functions $R:S^2 \to S^2$, where $S^2$ is the Riemann sphere. Our approach generalizes the degree formula for rational functions of complex polynomials,…
The Funk-Radon transform assigns to a function defined on the unit sphere its integrals along all great circles of the sphere. In this paper, we consider a frame decomposition of the Funk-Radon transform, which is a flexible alternative to…
Given a sequence of regular planar domains converging in the sense of kernel, we prove that the corresponding Green's functions converge uniformly on the complex sphere, provided the limit domain is also regular, and the connectivity is…
Contragenic functions are defined to be reduced-quaternion-valued harmonic functions which are orthogonal to all monogenic and antimonogenic functions in the $L^2$ norm of a given domain. The parallelism between the spaces of contragenic…
The new combined formulas have been established for the complex and real rotation-angular functions arising in the evaluation of two-center overlap integrals over arbitrary atomic orbitals in molecular coordinate system. These formulas can…
In this paper we study the Hilbert function of $\gr_{\mathfrak{m}}(R)$, when $R$ is a numerical semigroup ring or, equivalently, the coordinate ring of a monomial curve. In particular, we prove a sufficient condition for a numerical…
Unbounded (and bounded) Toeplitz operators (TO) with rational symbols are analysed in detail showing that they are densely defined closed and have finite dimensional kernels and deficiency spaces. The latter spaces as well as the domains,…