Abstract. In this paper we devise a new multi-dimensional integral transform within the Clifford analysis setting, the so-called Fourier-Bessel transform. It appears that in the two-dimensional case, it coincides with the Clifford-Fourier and cylindrical Fourier transforms introduced earlier. We show that this new integral transform satisfies operational formulae which are similar to those of t...

Method of calculation of space charge field of the beam using an expansion of space charge potential and space charge distribution as Fourier-Bessel series is discussed. Coefficients of series are connected by an algebraic equation, which substantially simplifies solution of the problem. Efficiency and accuracy of the method are discussed. Suggested method is effective in multidimensional probl...

in this paper, using a generalized translation operator, we prove theestimates for the generalized fourier-bessel transform in the space l2 on certainclasses of functions.

The standard harmonic balance method consists in expanding the displacement of an oscillator as a Fourier cosine series in time. A key modification is proposed here, in which the conservative force is additionally expanded as a Fourier sine series in space. As a result, the steady-state oscillation frequency can be expressed in terms of a Bessel series, and the sums of many such series are know...

We present an efficient and accurate algorithm for principal component analysis (PCA) of a large set of two-dimensional images and, for each image, the set of its uniform rotations in the plane and its reflection. The algorithm starts by expanding each image, originally given on a Cartesian grid, in the Fourier-Bessel basis for the disk. Because the images are essentially band limited in the Fo...

We present a new method for time-frequency representation (TFR), which combines a Fourier Bessel (FB) series expansion and the Wigner-Ville distribution (WVD). The FB series decomposes a multi-component signal into a number of single component signals before the WVD is applied. and then WVD is applied on the single component signals to analyze its time-frequency distribution (TFD). The simulati...

Received 28 June 2007, in final form 13 November 2007 Published 12 December 2007 Online at stacks.iop.org/JPhysA/41/015207 Abstract Various functions, defined as infinite series of products of Bessel functions of the first kind, are studied. Integral representations are obtained, and then used to deduce asymptotic approximations. Although several methods have been investigated (including power ...

In this paper, we present the q-Lidstone polynomials which are q-Bernoulli generated by third Jackson q-Bessel function, based on Green’s function of a certain q-difference equation. Also, provide q-Fourier series expansions these and derive some results related to them.

Some estimates are proved for the generalized Fourier-Bessel transform in the space (L^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.