We study an extension of the classical Paley-Wiener space structure, which is based on bilinear expansions of integral kernels into biorthogonal sequences of functions. The structure includes both sampling expansions and Fourier-Neumann type series as special cases. Concerning applications, several new results are obtained. From the Dunkl analogue of Gegenbauer’s expansion of the plane wave, we...

In this paper, we consider a new type of Bessel beams having Fourier-invariance property and, therefore, called Fourier-Bessel beams. contrast to the known beams, these have weak side lobes. Analytical expressions for complex amplitude proposed field in initial plane source and far region been obtained. It is shown that finite energy, although they do not Gaussian envelope. Their proportional f...

We study the heat equation in n dimensional by Diamond Bessel operator. We find the solution by method of convolution and Fourier transform in distribution theory and also obtain an interesting kernel related to the spectrum and the kernel which is called Bessel heat kernel.

In this paper we uses an I.I. Hirschman-W. Beckner entropy argument to give an uncertainty inequality for the q-Bessel Fourier transform: Fq,vf(x) = cq,v ∫ ∞ 0 f(t)jv(xt, q 2)t2v+1dqt, where jv(x, q) is the normalized Hahn-Exton q-Bessel function.

The technique of Bakhvalov and Vasil'eva for evaluating Fourier integrals is generalized to integrals involving exponential and Bessel functions.

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,...

It cannot be overstated how significant Series Equations are to the fields of pure and applied mathematics respectively. The majority mathematical topics revolve around use series. Virtually, in every subject mathematics, series play an important role. solutions a major role solution mixed boundary value problems. Dual, triple, quadruple equations useful finding four part problems electrostatic...

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...