On Abel-Tauber Theorems for Fourier Cosine Transforms

The Abel, Fourier and Radon transforms on symmetric spaces

In this paper we prove some recent results on the three transforms in the title and discuss their relationships to older results. The spaces we deal with are symmetric spaces X = G/K of the noncompact type, G being a connected noncompact semisimple Lie group with finite center and K a maximal compact subgroup. For the two natural Radon transforms on X we prove a new inversion formula and a shar...

Integral Transforms of Fourier Cosine Convolution Type

which has the following property Fc(f ∗ g)(x) = (Fcf)(x)(Fcg)(x). (3) The theory of integral transforms related to the Fourier and Mellin convolutions is well developed [2, 6, 10, 11, 12, 13, 19] and has many applications. Some other classes of integral transforms, that are not related to any known convolutions, are considered in [14, 15]. In this paper we investigate integral transforms of the...

Cosine Products, Fourier Transforms, and Random Sums

one gets the first actual formula for 7r that mankind ever discovered, dating from 1593 and due to Frangois Viete (1540-1603), whose Latinized name is Vieta. (Was any notice taken of the formula's 400th anniversary, perhaps by the issue of a postage stamp?) From the samples of a function t(x) at equally spaced points x", n E z, one can reconstruct the complete function with the aid of sin x/x, ...

Unified Architecture for Discrete Fourier and Inverse Cosine Transforms

A unified architecture for radix-2 decimation-in-time fast Fourier transform and inverse discrete cosine transform of type II is presented based on constant geometry formulation of the algorithms. The parallelism of the architecture can be specified to meet various throughput and area requirements. The type and size of the transform in the architecture can be configured in run-time. In addition...

Integral Transforms of Fourier Cosine and Sine Generalized Convolution Type