Related papers: Henstock--Kurzweil Fourier transforms

It has been proven in previous papers that each Henstock-Kurzweil-Pettis integrable multifunction with weakly compact values can be represented as a sum of one of its selections and a Pettis integrable multifunction. We prove here that if…

A rapid transformation is derived between spherical harmonic expansions and their analogues in a bivariate Fourier series. The change of basis is described in two steps: firstly, expansions in normalized associated Legendre functions of all…

The paper presents a new formula for the fractional integration, which generalizes the Riemann-Liouville and Hadamard fractional integrals into a single form, which when a parameter fixed at different values, produces the above integrals as…

We study Fourier and Laplace transforms for Fourier hyperfunctions with values in a complex locally convex Hausdorff space. Since any hyperfunction with values in a wide class of locally convex Hausdorff spaces can be extended to a Fourier…

We obtain a characterisation of the Fourier transform on the space of Schwartz class functions on $\mathbb{R}^n.$ The result states that any appropriately additive bijection of the Schwartz space onto itself, which interchanges convolution…

In many articles on the integral expressions of Mittag-Leffler functions, we have found that whether the integral expression can be used at the origin is still unresolved. In this article we give the applicable conditions and proof. And we…

In this article, we prove certain Weber-Schafheitlin type integral formulae for Bessel functions over complex numbers. A special case is a formula for the Fourier transform of regularized Bessel functions on complex numbers. This is applied…

Let F(R^n) be the algebra of Fourier transforms of functions from L_1(R^n), K(R^n) be the algebra of Fourier transforms of bounded complex Borel measures in R^n and W be Wiener algebra of continuous 2pi-periodic functions with absolutely…

It is proved by the method of partial fraction expansions and Sturm's oscillation theory that the zeros of certain Hankel transforms are all real and distributed regularly between consecutive zeros of Bessel functions. As an application,…

Elementary transformations of equations $A\psi=\lambda\psi$ are considered. The invertibility condition (Theorem 1) is established and similar transformations of Riccati equations in the case of second order differential operator $A$ are…

In this paper, we define a new transform called the Gabor quaternionic Fourier transform (GQFT), which generalizes the classical windowed Fourier transform to quaternion valued-signals, we give several important properties such as the…

Using Kakichev's classical concept and extending Yakubovich-Britvina's approach (\textit{Results. Math.} 55(1-2):175-197, 2009) and (\textit{Integral Transforms Spec. Funct.} 21(4):259--276, 2010) for setting up Kontorovich-Lebedev…

Fourier sine transforms containing irrational integrands are presented. Explicit closed form expressions are shown to be related to Lommel functions and in special cases to the Fresnel integrals. Such integrals arise in the semi-classical…

Let $\mu$ be a positive measure on the real line with locally finite support $\Lambda$ and integer masses such that its Fourier transform in the sense of distributions is a purely point measure. An explicit form is found for an entire…

Consider the (Helgason-) Fourier transform on a Riemannian symmetric space G/K. We give a simple proof of the L^p-Schwartz space isomorphism theorem (0 <p \le 2) for K-finite functions. The proof is a generalization of J.-Ph. Anker's proof…

We use the properties of Hermite and Kamp\'e de F\'eriet polynomials to get closed forms for the repeated derivatives of functions whose argument is a quadratic or higher-order polynomial. The results we obtain are extended to product of…

Iterative Fast Fourier Transform methods are useful for calculating the fields in composite materials and their macroscopic response. By iterating back and forth until convergence, the differential constraints are satisfied in Fourier…

The aim of this paper is to show that, in various situations, the only continuous linear map that transforms a convolution product into a pointwise product is a Fourier transform. We focus on the cyclic groups $\Z/nZ$, the integers $\Z$,…

We study relative integral functors for singular schemes and characterise those which preserve boundness and those which have integral right adjoints. We prove that a relative integral functor is an equivalence if and only if its…

Classic complex analysis is built on structural function $K=1$ only associated with Cauchy-Riemann equations, subsequently various generalizations of Cauchy-Riemann equations start to break this situation. The goal of this article is to…