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Szegö Polynomials on a Compact Group with Ordered Dual

Published online by Cambridge University Press:  20 November 2018

I. I. Hirschman Jr.
I. I. Hirschman Jr.*
Affiliation:
Stanford University and Washington University
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The Szegö polynomials are defined on T, the real numbers modulo 1. In this paper and in its sequel we give a generalization of Szegö polynomials in which T is replaced by an arbitrary locally compact abelian group θ on whose dual there has been distinguished a measurable order relation compatible with the group structure. The present paper is devoted to the case where θ is compact and therefore discrete. The general case will be taken up in the sequel mentioned above. It is desirable to proceed in this way because the case θ compact is much simpler and much more like the classical situation than is the general case, in which various measure-theoretic difficulties obtrude. Moreover, as it happens, it is possible to develop the theory in this way with relatively little repetition.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 538 - 560
Copyright
Copyright © Canadian Mathematical Society 1966

References

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