Related papers: Fourier Transform of some irrational integrands
In this paper we examine the existence of bicomplexified inverse Fourier transform as an extension of its complexified inverse version within the region of convergence of bicomplex Fourier transform. In this paper we use the idempotent…
These informal notes consider Fourier transforms on a simple class of nice functions and some basic properties of the Fourier transform.
The Harish-Chandra--Howe local character expansion expresses the characters of reductive, $p$-adic groups in terms of Fourier transforms of nilpotent orbital integrals on their Lie algebras, and Murnaghan--Kirillov theory expresses many…
This paper studies the effects on Zernike coefficients of aperture scaling, translation and rotation, when a given aberrated wavefront is described on the Zernike polynomial basis. It proposes a new analytical method for computing the…
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…
In this paper Fourier transform of multivariate orthogonal polynomials on the simplex is presented. A new family of multivariate orthogonal functions is obtained by using the Parseval's identity and several recurrence relations are derived.
The quadratic phase Fourier transform (QPFT) is a generalization of several well-known integral transforms, including the linear canonical transform (LCT), fractional Fourier transform (FrFT), and Fourier transform (FT). This paper…
One of the goals of the present paper is to propose an elementary method to find a general formula for the Fourier transform containing a pair of complex gamma functions with a monomial sm in terms of Gauss's hypergeometric functions 2F1.…
This report investigates the main definitions and fundamental properties of the fractional two-sided quaternionic Dunkl transform in two dimensions. We present key results concerning its structure and emphasize its connections to classical…
The Fourier transform is typically seen as closely related to the additive group of real numbers, its characters and its Haar measure. In this paper, we propose an alternative viewpoint; the Fourier transform can be uniquely characterized…
A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral…
Recently renewed interest in the Lobachevsky-type integrals and interesting identities involving the cardinal sine motivate an extension of the classical Parseval formula involving both periodic and non-periodic functions. We develop a…
In this paper, an open problem in the multidimensional complex analysis is pesented that arises in the investigation of the regularity properties of Fourier integral operators and in the regularity theory for hyperbolic partial differential…
Ultracold neutral bosons in a rapidly rotating atomic trap have been predicted to exhibit fractional quantum Hall-like states. We describe how the composite fermion theory, used in the description of the fractional quantum Hall effect for…
There are two formulations at non-zero chemical potential; one is the formulation that a Lagrangian includes a chemical potential, the other is the formulation that a Lagrangian does not include a chemical potential. The existence of two…
This manuscript introduces a generalization of the Mellin integral transform within the framework of weighted fractional calculus with respect to an increasing function. The proposed transform is much more suitable for working with…
A number of the Fourier Series which occur in the theory of the semi-classical atom due to Englert and Schwinger are generalized and presented.
We study the Fourier transform of polynomials in an orthogonal family, taken with respect to the orthogonality measure. Mastering the asymptotic properties of these transforms, that we call Fourier--Bessel functions, in the argument, the…
A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space…
We consider and discuss some basic properties of the bicomplex analog of the classical Bargmann space. The explicit expression of the integral operator connecting the complex and bicomplex Bargmann spaces is also given. The corresponding…