Zobrazeno 1 - 10
of 286
pro vyhledávání: '"33C50"'
Autor:
Zakharov, Victor G.
The generalization, similarly to exponential multivariate bases in the Fourier transform, of the Bessel functions to many dimensions is offered. Analogously to the Fourier transform property under the differentiation, the similar Hankel transform pro
Externí odkaz:
http://arxiv.org/abs/2410.14304
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 functions in
Externí odkaz:
http://arxiv.org/abs/2410.03623
In this paper, a finite set of biorthogonal polynomials in two variables is produced using Konhauser polynomials. Some properties containing operational and integral representation, Laplace transform, fractional calculus operators of this family are
Externí odkaz:
http://arxiv.org/abs/2408.07811
Autor:
Xu, Yuan
In his classical paper [5], Koornwinder studied a family of orthogonal polynomials of two variables, derived from symmetric polynomials. This family possesses a rare property that orthogonal polynomials of degree $n$ have $n(n+1)/2$ real common zeros
Externí odkaz:
http://arxiv.org/abs/2407.09903
Autor:
Greilhuber, Josef Eberhard
We show that, in dimension three and higher, the space of harmonic functions vanishing on the cone defined by a generically chosen harmonic quadratic polynomial is two-dimensional. This phenomenon is surprisingly robust, generalizing to arbitrary ell
Externí odkaz:
http://arxiv.org/abs/2407.07039
For a family of polynomials in two variables, orthogonal with respect to a weight function, we prove under some conditions, equivalence between: the Matrix Pearson equation of the weight, the second order linear partial differential equation, the ort
Externí odkaz:
http://arxiv.org/abs/2407.06995
In this paper we introduce Crouzeix-Raviart elements of general polynomial order $k$ and spatial dimension $d\geq2$ for simplicial finite element meshes. We give explicit representations of the non-conforming basis functions and prove that the confor
Externí odkaz:
http://arxiv.org/abs/2407.04361
Recently, \"Ozarslan and Elidemir (2023) introduced a methodology for constructing two-variable biorthogonal polynomial families with the help of one-variable biorthogonal and orthogonal polynomial families. The primary objective of the paper is to i
Externí odkaz:
http://arxiv.org/abs/2405.15043
Autor:
Marriaga, Misael E.
The aim of this work is to report on several ladder operators for generalized Zernike polynomials which are orthogonal polynomials on the unit disk $\mathbf{D}\,=\,\{(x,y)\in \mathbb{R}^2: \; x^2+y^2\leqslant 1\}$ with respect to the weight function
Externí odkaz:
http://arxiv.org/abs/2405.02988
Publikováno v:
Phys. Rev. D 109 (2024), 116015
We present a new exactly solvable case in strong-field QED with one-dimensional step potential (x-step). The corresponding x-step is given by an analytic asymmetric with respect to the axis x reflection function. The step can be considered as a certa
Externí odkaz:
http://arxiv.org/abs/2404.02640