Related papers: The $\rho$-Fourier transform

The Fourier transform of the indicator function of arbitrary polygons and polyhedra is computed for complex wavevectors. Using the divergence theorem and Stokes' theorem, closed expressions are obtained. Apparent singularities, all…

The paper develops theory of covariant transform, which is inspired by the wavelet construction. It was observed that many interesting types of wavelets (or coherent states) arise from group representations which are not square integrable…

Projections are constructed in the rotation algebra that are orthogonal to their Fourier transform and which are fixed under the flip automorphism. Such projections are expected in a construction of an inductive limit structure for the…

Using the structure of the Boson-Fermion Fock space and an argument taken from [2], we give a new proof of the triviality of the $L^2$ cohomology groups on an abstract Wiener space, alternative to that given by Shigekawa [9]. We apply some…

Boehmians are quotients of sequences which are constructed by using a set of axioms. In particular, one of these axioms states that the set $S$ from which the {\it denominator} sequences are formed should be a commutative semigroup with…

An additive fast Fourier transform over a finite field of characteristic two efficiently evaluates polynomials at every element of an $\mathbb{F}_2$-linear subspace of the field. We view these transforms as performing a change of basis from…

We develop a Galois descent approach to finite-field Fourier spectra over an arbitrary finite base field. Let $\mathbb K=\mathbb F_q$ and $\mathbb L=\mathbb F_{q^m}$. If a Fourier transform is applied to a $\mathbb K$-valued vector, then…

Conjectures of Braverman and Kazhdan, Ng\^o and Sakellaridis have motivated the development of Schwartz spaces for certain spherical varieties. We prove that under suitable assumptions these Schwartz spaces are naturally a representation of…

We prove that if $\rho: A(H) \to B(G)$ is a homomorphism between the Fourier algebra of a locally compact group $H$ and the Fourier-Stieltjes algebra of a locally compact group $G$ induced by a mixed piecewise affine map $\alpha : G \to H$,…

S.Block and H.Esnault constructed the local Fourier transform for D-modules. We present a different approach to the local Fourier transform, which makes its properties almost tautological. We apply the local Fourier transform to compute the…

Let n >1 be an integer, and G a doubly transitive subgroup of the symmetric group on X={1,...,n}. In this paper we find all linear group representations rho of G on an euclidean vector space V which contains a set of equiangular vector…

Fractional supersymmetry denotes a generalisation of supersymmetry which may be constructed using a single real generalised Grassmann variable, $\theta = \bar{\theta}, \, \theta^n = 0$, for arbitrary integer $n = 2, 3, ...$. An explicit…

A geometric generalization of first-order Lagrangian formalism is used to analyse a conformal field theory for an arbitrary primary field. We require that global conformal transformations are Noetherian symmetries and we prove that the…

Following ideas of G. Moore and G. Segal, we explicitly construct a G-equivariant topological field theory from an arbitrary Frobenius algebra equipped with a twisted action of a finite group G.

Starting from square-integrable wave functions on a Lie group, we build an invertible Fourier transform mapping them on wave functions on the dual of the Lie algebra. This is a group-theoretic version of the map from position space to…

Let $G$ be the universal Chevalley-Demazure group scheme corresponding to a reduced irreducible root system of rank $\geq 2$, and let $R$ be a commutative ring. We analyze the linear representations $\rho \colon G(R)^+ \to GL_n (K)$ over an…

We define an approximate version of the Fourier transform on $2^L$ elements, which is computationally attractive in a certain setting, and which may find application to the problem of factoring integers with a quantum computer as is…

For any finite group G we define the moduli space of pointed admissible G-covers and the concept of a G-equivariant cohomological field theory (G-CohFT), which, when G is the trivial group, reduce to the moduli space of stable curves and a…

There is a canonical unitary transformation from $L^2(\R)$ onto the Fock space $F^2$, called the Bargmann transform. We study the action of the Bargmann transform on several classical integral operators on $L^2(\R)$, including the…

A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. Whereas the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, the covariant canonical transformation…