Citation
Ryan, Robert Dean (1960) Fourier transforms of certain classes of integrable functions. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd06152006085338
Abstract
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Let G be a locally compact Abelian group with character group [...]. M(G) will denote the class of all bounded Radon measures on G and P(G) will denote the class of all continuous positive definite functions on G. For [...] we write [...] = [...] and for [...] we write [...] = [...]. [...] will denote the linear space spanned by [...]. We find necessary and sufficient conditions on [...] in order that [...] for [...]. Theorem 5, Chapter II: [...] for [...] if and only if there exists a constant K > 0 such that [...] for all [...] where [...]. Theorem 6, Chapter II: [...] for [...] if and only if [...] for all [...]. Theorems 3 and 4, Chapter III: [...] if and only if there exists some p, [...], such that for each [...] > 0 there exists a [...] > 0 with the property that [...] whenever [...] and [...]. By taking G to be the unit circle and p = 2 in Theorems 3 and 4, Chapter III, we obtain a generalization of a theorem by R. Salem (Comptes Rendus Vol. 192 (1931)). Taking G to be the additive group of reals and p = 1 gives a generalization of a theorem by A. Berry (Annals of Math. (2) Vol. 32 (1931)).
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:  1 January 1960 
Record Number:  CaltechETD:etd06152006085338 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd06152006085338 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  2609 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  29 Jun 2006 
Last Modified:  26 Dec 2012 02:53 
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