Related papers: Operational calculus for Fourier transform on the …

Massive on-shell operator matrix elements and self-energy diagrams with outer gluon lines are calculated analytically at $O(\alpha_s^2)$, using Mellin-Barnes integrals and representations through generalized hypergeometric functions. This…

Let a finite group $G$ act on the complex plane $({\Bbb C}^2, 0)$. We consider multi-index filtrations on the spaces of germs of holomorphic functions of two variables equivariant with respect to 1-dimensional representations of the group…

We present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite group. By extending work which connects Bratteli diagrams to the construction of Fast…

Circular and hyperbolic fractional-order Fourier transformations are actually Weyl pseudo-differential operators. Their associated kernels and symbols are written explicitly. Products of fractional-order Fourier transformations are obtained…

The group $GL(2,Z)$ acts in a natural way on the set of pairs of $n\times n$-matrices determined up to a simultaneous conjugation. For $n=3$ we write explicit formulas for action of generators of $GL(2,Z)$ in the terms of spectral data of…

We show how to compute conformal blocks of operators in arbitrary Lorentz representations using the formalism described in arXiv:1905.00036 and arXiv:1905.00434, and present several explicit examples of blocks derived via this method. The…

We construct a two-parameter family of actions \omega_{k,a} of the Lie algebra sl(2,R) by differential-difference operators on R^N \setminus {0}. Here, k is a multiplicity-function for the Dunkl operators, and a>0 arises from the…

We introduce the concepts of the Fourier transform and convolution generated by an arbitrary restriction of the differentiation operator in the space $L_{2}(0,b).$ In contrast to the classical convolution, the introduced convolution…

We consider the bilinear Fourier multiplier operator with the multiplier written as a linear combination of a fixed bump function. For those operators we prove two transference theorems, one in amalgam spaces and the other in Wiener amalgam…

Let H be a Schrodinger operator on the real line, where the potential is in L^1 and L^2. We define the perturbed Fourier transform F for H and show that F is an isometry from the absolute continuous subspace onto L^2. This property allows…

We obtain an explicit classification of all $2\times 2$ real hypergeometric Bochner pairs, ie. pairs $(W(x),\mathfrak{D})$ consisting of a $2\times 2$ real hypergeometric differential operator $\mathfrak{D}$ and a $2\times 2$ weight matrix…

We give two algebro-geometric inspired approaches to fast algorithms for Fourier transforms in algebraic signal processing theory based on polynomial algebras in several variables. One is based on module induction and one is based on a…

In this paper, we prove that slice polyanalytic functions on quaternions can be considered as solutions of a power of some special global operator with nonconstant coefficients as it happens in the case of slice hyperholomorphic functions.…

This paper introduces a factorization for the inverse of discrete Fourier integral operators that can be applied in quasi-linear time. The factorization starts by approximating the operator with the butterfly factorization. Next, a…

In this paper, we give explicit expressions of differential-difference operators appeared in the hypothesis of the general Fourier multiplier theorem associated to the Heisenberg groups proved by Mauceri and De Micheal for one dimension and…

We discuss the spectral decomposition of the hypergeometric differential operators on the line $\mathrm{Re}\, z=1/2$. Such operators arise in the problem of decomposition of tensor products of unitary representations of the universal…

We consider series expansions in bases of classical orthogonal polynomials. When such a series solves a linear differential equation with polynomial coefficients, its coefficients satisfy a linear recurrence equation. We interpret this…

For a general ordinary differential operator $\mathcal{L}$ with periodic coefficients we prove that the characteristic polynomial of the Floquet matrix is irreducible over the field of meromorphic functions. We also consider a multipoint…

Through examples, we illustrate how to compute differential operators on a quotient of an affine semigroup ring by a radical monomial ideal, when working over an algebraically closed field of characteristic 0.

In this paper we develop elements of the global calculus of Fourier integral operators in $R^n$ under minimal decay assumptions on phases and amplitudes. We also establish global weighted Sobolev $L^2$ estimates for a class of Fourier…