Related papers: Compactly supported, orthogonal, continuous piecew…
We study counting functions of planar polygons arising from homological mirror symmetry of elliptic curves. We first analyze the signature and rationality of the quadratic forms corresponding to the signed areas of planar polygons. Then we…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
This is a review of ($q$-)hypergeometric orthogonal polynomials and their relation to representation theory of quantum groups, to matrix models, to integrable theory, and to knot theory. We discuss both continuous and discrete orthogonal…
We use Lorentz polynomials to present the solutions explicitly of equations (6.1.7) of [I. Daubechies, Ten lectures on wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, 61. Society for Industrial and Applied Mathematics…
Motivated by the work on hypergeometric summation theorems (recorded in the table III of Prudnikov et al. pp. 541-546), we have established some new summation theorems for Clausen's hypergeometric functions with unit argument in terms of…
High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the…
From the literature it is known that orthogonal polynomials as the Jacobi polynomials can be expressed by hypergeometric series. In this paper, the authors derive several contiguous relations for terminating multivariate hypergeometric…
In this paper we study the additive splitting associated to the quaternionic Cauchy transform defined by the Cauchy formula of slice hyperholomorphic functions. Moreover, we introduce and study the analogue of the fundamental solution of…
Extension problems for polynomial valuations on different cones of convex functions are investigated. It is shown that for the classes of functions under consideration, the extension problem reduces to a simple geometric obstruction on the…
It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…
We summarize two geometrical approaches to analytically evaluate higher-fold Mellin-Barnes (MB) integrals in terms of hypergeometric functions. The first method is based on intersections of conic hulls, while the second one, which is more…
Cubic and quartic non-autonomous differential equations with continuous piecewise linear coefficients are considered. The main concern is to find the maximum possible multiplicity of periodic solutions. For many classes, we show that the…
The multiresolution analysis of Alpert is considered. Explicit formulas for the entries in the matrix coefficients of the refinement equation are given in terms of hypergeometric functions. These entries are shown to solve generalized…
We give a technical overview of our exact-real implementation of various representations of the space of continuous unary real functions over the unit domain and a family of associated (partial) operations, including integration, range…
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…
This current article aims to study a new subclass of meromorphic functions with positive coefficients by reconstructing a new operator in the punctured open disc. Also, some geometric properties are considered and investigated, such results…
Conventional functional/path integrals used in physics are most often defined and understood, either explicitly or implicitly, as the infinite-dimensional analog of Fourier transform. In this paper, the infinite-dimensional analog of Mellin…
Through the study of novel variants of the classical Littlewood-Paley-Stein $g$-functions, we obtain pointwise estimates for broad classes of highly-singular Fourier multipliers on $\mathbb{R}^d$ satisfying regularity hypotheses adapted to…
Recently the construction of various integral transforms for slice monogenic functions has gained a lot of attention. In line with these developments, the article at hand introduces the slice Fourier transform. In the first part, the kernel…
The c-functions, related to a reductive symmetric space G/H and a fixed representation of a maximal compact subgroup K of G, are shown to satisfy polynomial bounds in imaginary directions.