Related papers: Compactly supported, orthogonal, continuous piecew…
We present the applications of variation -- wavelet analysis to polynomial/rational approximations for orbital motion in transverse plane for a single particle in a circular magnetic lattice in case when we take into account multipolar…
This paper addresses two primary objectives in the realm of classical multiple orthogonal polynomials with an arbitrary number of weights. Firstly, it establishes new and explicit hypergeometric expressions for type I Hahn multiple…
A relaxed factorization is used to obtain many of the properties obeyed by the confluent hypergeometric functions. Their implications on the analytical solutions of some interesting physical problems are also studied. It is quite remarkable…
Slice-regular functions of a quaternionic variable have been studied extensively in the last 12 years, resulting, in many ways, quite close to classical holomorphic functions of a complex variable; indeed, there is a correspondence between…
We consider several systems of algebras of real- and complex-valued functions, which appear in o-minimal geometry and related geometrically tame contexts. For each such system, we prove its stability under parametric integration and we…
Functions of several octonion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the ${\tilde {\partial}}$-equations are studied. More generally functions of several…
We investigate several families of multiple orthogonal polynomials associated with weights for which the moment generating functions are hypergeometric series with slightly varying parameters. The weights are supported on the unit interval,…
Multiple-integral representations of the (skew-)Macdonald symmetric functions are obtained. Some bosonization schemes for the integral representations are also constructed.
We provide a representation of the $C^*$-algebra generated by multidimensional integral operators with piecewise constant kernels and discrete ergodic operators. This representation allows us to find the spectrum and to construct the…
In the paper, we present a family of multivariate compactly supported scaling functions, which we call as elliptic scaling functions. The elliptic scaling functions are the convolution of elliptic splines, which correspond to homogeneous…
The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the authors provide a general introduction to the umbral version of…
Exactly solvable two-dimensional polygon models, counted by perimeter and area, are described by $q$-algebraic functional equations. We provide techniques to extract the scaling behaviour of these models up to arbitrary order and apply them…
This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier…
Spectral representations of the dilation and translation operators on $L^2({\mathbb R})$ are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions…
The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear…
We present integral representations of solutions to division problems involving matrices of polynomials in several complex variables. We also find estimates of the polynomial degree of the solutions by means of careful degree estimates of…
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…
Multiscale periodic homogenization is extended to an Orlicz-Sobolev setting. It is shown by the reiteraded periodic two-scale convergence method that the sequence of minimizers of a class of highly oscillatory minimizations problems…
Multivariate piecewise polynomial functions (or splines) on polyhedral complexes have been extensively studied over the past decades and find applications in diverse areas of applied mathematics including numerical analysis, approximation…
A new class of bivariate poly-analytic Hermite polynomials is considered. We show that they are realizable as the Fourier-Wigner transform of the univariate complex Hermite functions and form a nontrivial orthogonal basis of the classical…