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Submission for the degree of Doctor of Science


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Bloom, Walter R 1993 , 'Submission for the degree of Doctor of Science', Coursework Master thesis, University of Tasmania.

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My research lies in harmonic analysis, overlapping the areas of pure and applied
mathematics, and over the last twenty years has developed along two major themes:
(a) Abstract approximation and multiplier theory
(b) Hypergroups and probability theory
In addition I have been active in:
(c) Mathematics education and other areas
My work in abstract approximation and multiplier theory began with my doctoral
studies on Bernstein's inequality for locally compact groups. An important
breakthrough was to prove versions of this inequality based purely on properties of
group translation, and without any reference to a differential structure. This led to
versions of the Jackson and Bernstein theorems estimating the degree of
approximation of smooth functions by partial sums of their Fourier series. An integral
part of these developments was a study of multiplier theory for various related spaces
of functions.
During the past ten years my research has been in hypergroups and probability theory
on these spaces. Much of this work has been done in collaboration with Herbert
Heyer, and covers a study of the properties of the Fourier transform and convolution,
through to the development of properties of positive definite and negative definite
functions. As part of this work a major activity of the past five years has been the
preparation (jointly with Herbert Heyer) of a substantial research monograph
Harmonic analysis of probability measures on hypergroups which will be published
by Walter de Gruyter publishers this year.
This thesis covers those publications listed under (a) and (b) that have appeared in

Item Type: Thesis - Coursework Master
Authors/Creators:Bloom, Walter R
Keywords: Mathematics, Mathematics
Copyright Holders: The Author
Copyright Information:

Copyright 1993 the Author - The University is continuing to endeavour to trace the copyright owner(s) and in the meantime this item has been reproduced here in good faith. We would be pleased to hear from the copyright owner(s).

Additional Information:

Thesis (D.Sc.)--University of Tasmania, 1994. Includes bibliographical references

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