where φ :Rn → C and φt(x)= t−nφ(x/t), t > 0. For conditions of validity of identity (1.1), we may refer to [3]. Hankel convolution introduced by Hirschman Jr. [5] related to the Hankel transform was studied at length by Cholewinski [1] and Haimo [4]. Its distributional theory was developed byMarrero and Betancor [6]. Pathak and Pandey [8] used Hankel convolution in their study of pseudodifferen...

 sinx x if x 6= 0 1 otherwise This function is important in many areas of computing science, approximation theory, and numerical analysis. For example, it is used in interpolation and approximation of functions, approximate evaluation of transforms (e.g. Hilbert, Fourier, Laplace, Hankel, and Mellon transforms as well as the fast Fourier transform). It is used in finding approximate solutions ...

The method originally proposed by Yu et al. [Opt. Lett. 23, 409 (1998)] for evaluating the zero-order Hankel transform is generalized to high-order Hankel transforms. Since the method preserves the discrete form of the Parseval theorem, it is particularly suitable for field propagation. A general algorithm for propagating an input field through axially symmetric systems using the generalized me...

Let m have compact support in (0,∞). For 1 < p < 2d/(d + 1), we give a necessary and sufficient condition for the Lprad(R )-boundedness of the maximal operator associated with the radial multiplier m(|ξ|). More generally we prove a similar result for maximal operators associated with multipliers of modified Hankel transforms. The result is obtained by modifying the proof of the characterization...

In this paper we prove $$L^p$$ estimates for Stein’s square functions associated with Fourier–Bessel expansions. Furthermore, transference results from series to Hankel transforms. Actually, these are vector-valued multipliers discrete continuous in the Bessel setting. As a consequence, deduce sharpness of range p -boundedness corresponding property Hankel–Stein functions. Finally, that ones ha...

This paper presents a fast algorithm for bidiagonalizing a Hankel matrix. An m×n Hankel matrix is reduced to a real bidiagonal matrix in O((m+ n)n log(m+ n)) floating-point operations (flops) using the Lanczos method with modified partial orthogonalization and reset schemes to improve its stability. Performance improvement is achieved by exploiting the Hankel structure, as fast Hankel matrix–ve...

In this paper, we present a systematic study of the various characteristics and properties some continuous discrete fractional Bessel wavelet transforms. The method is based upon theory Hankel transform.

We deal with a class of one-parameter family integral transforms Bargmann type arising as dual transform fractional Hankel transform. Their ranges are identified to be special subspaces of...