GENERALIZED FOURIER-WIENER FUNCTION SPACE TRANSFORMS

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 ...

Generalized Fourier Transforms of Distributions

In [1], R. A. Kunze has presented a notion of generalized Fourier transform of functions on locally compact abelian groups. The point of this paper is to extend this idea in the direction of distribution theory and to present some initial results on this generalized Fourier transform of distributions. In a later paper we hope to investigate in detail the domain, range, and kernel of this transf...

Linear and nonlinear generalized Fourier transforms.

This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields a generalization and unification of various fundamental mathematical techniques and, in particular, it yields an extension of the Fourier transform method.

Generalized Fourier Transforms and their Applications

This thesis centers around a generalization of the classical discrete Fourier transform. We first present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite group or semisimple algebra. By extending work which connects Bratteli diagrams to the construction of Fast Fourier Transform algorithms [2], we make exp...

Integral Transforms of Fourier Cosine and Sine Generalized Convolution Type