The method of realizing certain self-reciprocal transforms as (absolute) scattering, previously presented in summarized form in the case of the Fourier cosine and sine transforms, is here applied to the self-reciprocal transform f(y) 7→ H(f)(x) = ∫∞ 0 J0(2 √ xy)f(y) dy, which is isometrically equivalent to the Hankel transform of order zero and is related to the functional equations of the Dede...

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...

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, the two-dimensional triangular orthogonal functions (2d-tfs) are applied for solving a class of nonlinear two-dimensional volterra integral equations. 2d-tfs method transforms these integral equations into a system of linear algebraic equations. the high accuracy of this method is verified through a numerical example and comparison of the results with the other numerical methods.

We derive a general expression for the Hankel determinants of a Dirichlet series F (s) and derive the asymptotic behavior for the special case that F (s) is the Riemann zeta function. In this case the Hankel determinant is a discrete analogue of the Selberg integral and can be viewed as a matrix integral with discrete measure. We brie y comment on its relation to Plancherel measures.

In this paper, we study the finite Hankel transformation on spaces of generalized functions by developing a new procedure. We consider two Hankel type integral transformations hμ and h∗μ connected by the Parseval equation