Group invariant finite Fourier transforms.

Title: Group invariant finite Fourier transforms.
Identifier: AAI8821119
identifier: 8821119
Creator: Shenefelt, Myoung Hee.
Contributor: Adviser: Louis Auslander
Date: 1988
Language: English
Publisher: City University of New York.
Subject: Mathematics | Chemistry, Biochemistry | Biogeochemistry
Abstract: The computation of the finite Fourier transform of functions is one of the most used computations in crystallography. Since the Fourier transform involved is 3-dimensional, the size of the computation becomes very large even for relatively few sample points along each edge. In this thesis, there is a family of algorithms that reduce the computation of Fourier transform of functions respecting the symmetries. Some properties of these algorithms are: (1) The algorithms make full use of the group of symmetries of a crystal. (2) The algorithms can be factored and combined according to the prime factorization of the number of points in the sample space. (3) The algorithms are orginized into a family using the group structure of the crystallographic groups to make iterative procedures possible.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.