Related papers: Calculation of local formal Fourier transforms
This is the direct continuation of the paper "Mapping properties of Fourier transforms" (arXiv:2112.04896) using the same notation as there without further explanations. It deals with continuous and compact mappings of the Fourier transform…
The Replica Fourier Transform introduced previously is related to the standard definition of Fourier transforms over a group. Its use is illustrated by block-diagonalizing the eigenvalue equation of a four-replica Parisi matrix.
An experiment to demonstrate the Fourier transform of an electric signal using the Kundt's tube is described. The results of finding the component frequencies and an approximation to the amplitudes of two sinusoidal signals which compose an…
In this paper, the fractal calculus of fractal sets and fractal curves are compared. The analogues of the Riemann-Liouville and the Caputo integrals and derivatives are defined for the fractal curves which are non-local derivatives. The…
We show how to compute the Lagrangian Floer homology in the one-point blow up of the proper transform of Lagrangians submanifolds, solely in terms of information of the base manifold. As an example we present an alternative computation of…
In the present paper, a generalized local Taylor formula with the local fractional derivatives (LFDs) is proposed based on the local fractional calculus (LFC). From the fractal geometry point of view, the theory of local fractional…
The calculation of the hot plasma bound-free opacity according to the average atom models often leads to a noticeable effect of initial configuration on the shell ionization threshold. For the related problem of taking into account the…
This article is concerned with a new method for the approximate evaluation of Fourier sine and cosine transforms. We develop and analyse a new quadrature rule for Fourier sine and cosine transforms involving transforming the integral to one…
Let $G$ be an even orthogonal quasi-split group defined over a local non-archimedean field $F$. We describe the subspace of smooth vectors of the minimal representation of $G(F),$ realized on the space of square-integrable functions on a…
In this paper, we introduce the fractional Fourier series on the fractional torus and study some basic facts of fractional Fourier series, such as fractional convolution and fractional approximation. Meanwhile, fractional Fourier inversion…
We use weakly holomorphic modular forms for the Hecke theta group to construct an explicit interpolation formula for Schwartz functions on the real line. The formula expresses the value of a function at any given point in terms of the…
We compare two different methods of computing form factors. One is the well established procedure of solving the form factor consistency equations and the other is to represent the field content as well as the particle creation operators in…
This paper examines the existence and region of convergence of Fourier transform of the functions of bicomplex variables with the help of projection on its idempotent components as auxiliary complex planes. Several basic properties of this…
A partial fraction decomposition of the Fermi function resulting in a finite sum over simple poles is proposed. This allows for efficient calculations involving the Fermi function in various contexts of electronic structure or electron…
Discrete analogs of the classical Fourier-Jacobi transform are introduced and investigated. It involves series and integrals with respect to parameters of the Gauss hypergeometric function ${}_2F_1(a+in/2,a-in/2;\ c; -x^2 ), \ x >0, n \in…
In this article, we develop comprehensive frequency domain methods for estimating and inferring the second-order structure of spatial point processes. The main element here is on utilizing the discrete Fourier transform (DFT) of the point…
In this paper we propose a new formulation of the Fourier Modal Method based on an alternative treatment of interface conditions allowing us to overcome the effect of the Gibbs phenomenon. Explicit consideration of the interface conditions…
Fast Fourier transforms are used to develop algorithms for the fast generation of correlated Gaussian random fields on d-dimensional rectangular regions. The complexities of the algorithms are derived, simulation results and error analysis…
For any finite group $G$, we give an arithmetic algorithm to compute generalized Discrete Fourier Transforms (DFTs) with respect to $G$, using $O(|G|^{\omega/2 + \epsilon})$ operations, for any $\epsilon > 0$. Here, $\omega$ is the exponent…
Modern programmable digital signal processing relies on floating-point numbers for their ease of use. Fixed-point number formats have the potential to save resources and improve execution time, but realising this potential burdens the…