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Generalized multipliers on locally compact Abelian groups

Citation

Ford, Lawrence Charles (1974) Generalized multipliers on locally compact Abelian groups. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-10122005-082659

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.

Let G be a locally compact Abelian group with dual [...], [...], and [...] supp [...] is compact}. Then for [...], the containments are proper if G is noncompact, and [...] is a dense, translation invariant subspace of [...] for [...]. Let [...] be a complex valued function defined on [...], and [...] = [...]. Suppose [...]. Define the operator, [...] by the equation [...] for each [...]. Then [...] is a module over M(G), [...] is a module homomorphism, and [...] is (p, q) closed. We call [...] a generalized (p, q) multiplier.

The main results include:

(1) Suppose T is an operator satisfying: (a) The domain D(T) is a translation invariant subspace of [...], and the range R(T) [...]; (b) D(T) [...]; (c) T is (p, q) closed, linear, and commutes with all translations; (d) C X T(C) is dense in [...]. Then T = [...] for some [...].

(2) The set of all generalized (p, q) multipliers, denoted [...], is a linear space, and the set of all generalized (p, p) multipliers, denoted [...], is an algebra containing [...] and contained in [...].

(3) If [...], then [...] is locally the transform of a bounded (p, q) multiplier.

Further sections include a deeper study of [...], [...], and special results obtainable for compact G.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • DePrima, Charles R. (advisor)
  • Luxemburg, W. A. J. (advisor)
Thesis Committee:
  • Unknown, Unknown
Defense Date:7 February 1974
Record Number:CaltechETD:etd-10122005-082659
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-10122005-082659
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4041
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:14 Oct 2005
Last Modified:26 Dec 2012 03:04

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