Abstract. The aim of this paper is to establish an analogue of Logvinenko-Sereda’s theorem for the Fourier-Bessel transform (or Hankel transform) Fα of order α > −1/2. Roughly speaking, if we denote by PWα(b) the Paley-Wiener space of L -functions with FourierBessel transform supported in [0, b], then we show that the restriction map f → f |Ω is essentially invertible on PWα(b) if and only if Ω...

Abstract Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large self-adjoint random matrices from the generalized unitary ensembles. This paper considers discrete Tracy–Widom operators, and gives sufficient conditions for a discrete integrable operator to be the square of a Hankel matrix. Examples include the discrete Bessel kerne...

Using a generalized translation operator, we obtain a generalization of Theorem 5 in [4] for the Bessel transform for functions satisfying the (delta;gamma ; 2)-BesselLipschitz condition in L_{2;alpha}(R+).  

In this paper, we report the efficiency of Fourier Bessel transform and time-frequency based method in conjunction with the fractional Fourier transform, for extracting micro-Doppler radar signatures from the rotating targets. This approach comprises mainly of two processes; the first being decomposition of the radar return, in order to extract micro-Doppler (m-D) features and the second being,...

We consider a topological integral transform of Bessel (concentric isospectral sets) type and Fourier (hyperplane isospectral sets) type, using the Euler characteristic as a measure. These transforms convert constructible Z-valued functions to continuous R-valued functions over R n. Core contributions include: the definition of the topological Bessel transform; a relationship in terms of the lo...

We establish the inverse Lebedev expansion with respect to parameters and arguments of the modified Bessel functions for an arbitrary function from Hardy’s space H2,A, A> 0. This gives another version of the Fourier-integral-type theorem for the Lebedev transform. The result is generalized for a weighted Hardy space Ĥ2,A ≡ Ĥ2((−A,A);|Γ(1+Rez+iτ)|2dτ), 0 < A < 1, of analytic functions f(z),z = R...

&lt;p style='text-indent:20px;'&gt;In this article, we have investigated certain definite integrals and various integral transforms of the generalized multi-index Bessel function, such as Euler transform, Laplace Whittaker K-transform Fourier transforms. Also found applications problem on fractional kinetic equation pertaining to function using Sumudu transform technique. Mittage-Leffler is use...

A fast and numerically stable algorithm is described for computing the discrete Hankel transform of order 0 as well as evaluating Schlömilch and Fourier–Bessel expansions in O(N(logN)2/ loglogN) operations. The algorithm is based on an asymptotic expansion for Bessel functions of large arguments, the fast Fourier transform, and the Neumann addition formula. All the algorithmic parameters are se...

The paper presents calculations for the radiation of a loop antenna wrapped around a metallic cylinder into a conductive medium. The problem has been solved analytically by using Fourier transform and Bessel functions. The evaluation of the analytical solution, involves the use of exponentially scaled Bessel functions, and FFT to evaluate inverse Fourier transform, with all computations done in...

In this work, we are interested by the q-Bessel Fourier transform with a new approach. Many important results of this q-integral transform are proved with a new constructive demonstrations and we establish in particular the associated q-Fourier-Neumen expansion which involves the q-little Jacobi polynomials.