CaltechTHESIS
  A Caltech Library Service

Fourier transforms of certain classes of integrable functions

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:etd-06152006-085338

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 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):
  • Luxemburg, W. A. J.
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1960
Record Number:CaltechETD:etd-06152006-085338
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-06152006-085338
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 ETD-db
Deposited On:29 Jun 2006
Last Modified:26 Dec 2012 02:53

Thesis Files

[img]
Preview
PDF (Ryan_rd_1960.pdf) - Final Version
See Usage Policy.

2661Kb

Repository Staff Only: item control page