Generalized finite Fourier cosine transforms.

Integral Transforms of Fourier Cosine and Sine Generalized Convolution Type

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, ...

Sparse Generalized Fourier Transforms ∗

Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences. By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via a sparse variant ...

Intersection Bodies and Generalized Cosine Transforms

Intersection bodies represent a remarkable class of geometric objects associated with sections of star bodies and invoking Radon transforms, generalized cosine transforms, and the relevant Fourier analysis. We review some known facts and give them new proofs. The main focus is interrelation between generalized cosine transforms of different kinds and their application to investigation of certai...