Related papers: A family of convolution operators, part two
The functor of second quantization as well as quadratic creation and annihilation operators on the bosonic Fock space are defined through possibly infinite series. The domain of convergence is investigated by precise number operator…
The present paper, is devoted to investigation of operator--valued Fourier multiplier theorems from $B_{q_{1},r}^{s}$ to $B_{q_{2},r}^{s}$, optimal embedding of Besov spaces, the separability and positivity of differential operators. Here,…
We begin with an overview on square functions for spherical and Bochner-Riesz means which were introduced by Eli Stein, and discuss their implications for radial multipliers and associated maximal functions. We then prove new endpoint…
In this paper we extend our previous result on the description of the partcle motion in a generalized Heisenberg picture to a relativistic fermion. The operators of the Lorentz algebra in this picture may be regarded as field operators. In…
We discuss the simultaneous diagonalization of a family of commuting difference operators by Koornwinder's multivariable generalization of the Askey-Wilson polynomials. The operators constitute a complete set of quantum integrals for a…
The aim of this article is to define some new families of the special numbers. These numbers provide some further motivation for computation of combinatorial sums involving binomial coefficients and the Euler kind numbers of negative order.…
Fourier transform of multivariate orthogonal polynomials on the unit ball are obtained. By using Parseval's identity, a new family of multivariate orthogonal functions are introduced. The results are expressed in terms of the continuous…
We introduce the notion of a family of convolution operators associated with a given elliptic partial differential operator. Such a convolution structure is shown to exist for a general class of Laplace-Beltrami operators on two-dimensional…
Parametric factorizations of linear partial operators on the plane are considered for operators of orders two, three and four. The operators are assumed to have a completely factorable symbol. It is proved that ``irreducible'' parametric…
We review the properties of transversality of distributions with respect to submersions. This allows us to construct a convolution product for a large class of distributions on Lie groupoids. We get a unital involutive algebra…
For the Fourier Algebra of SL(2,R) any bounded multiplier is completely bounded.
The goal of this paper is to introduce the notion of polyconvolution for Fourier-cosine, Laplace integral operators, and its applications. The structure of this polyconvolution operator and associated integral transforms are investigated in…
We obtain new multilinear multiplier theorems for symbols of restricted smoothness which lie locally in certain Sobolev spaces. We provide applications concerning the boundedness of the commutators of Calder\'on and…
We study the shifted convolution sum of the divisor function and some other arithmetic functions.
We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…
We consider a weighted form of the Poisson summation formula. We prove that under certain decay rate conditions on the weights, there exists a unique unitary Fourier-Poisson operator which satisfies this formula. We next find the diagonal…
Motivated by the problem of spherical summability of products of Fourier series, we study the boundedness of the bilinear Bochner-Riesz multipliers $(1-|\xi|^2-|\eta|^2)^\delta_+$ and we make some advances in this investigation. We obtain…
We explore boundedness properties in the context of metric measure spaces, of some natural operators of convolution type whose study is suggested by certain transformations used in computer vision.
Under the assumption that orthogonal polynomials of several variables admit an addition formula, we can define a convolution structure and use it to study the Fourier orthogonal expansions on a homogeneous space. We define a maximal…
In this note a Fuglede type theorem is proved for Fourier multiplier operators on translation invariant Banach function spaces with order continuous norm over compact abelian groups.