Citation
Ford, Lawrence Charles (1974) Generalized multipliers on locally compact Abelian groups. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/NB311Y34. https://resolver.caltech.edu/CaltechETD:etd10122005082659
Abstract
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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): 

Thesis Committee: 

Defense Date:  7 February 1974 
Record Number:  CaltechETD:etd10122005082659 
Persistent URL:  https://resolver.caltech.edu/CaltechETD:etd10122005082659 
DOI:  10.7907/NB311Y34 
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 ETDdb 
Deposited On:  14 Oct 2005 
Last Modified:  21 Dec 2019 02:57 
Thesis Files

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