Accession Number : AD0726032

Title :   Investigations in Harmonic Analysis, Ergodic Theory and Related Topics in Analysis.

Descriptive Note : Final technical rept. Feb 70-Apr 71,

Corporate Author : HEBREW UNIV JERUSALEM (ISRAEL)

Personal Author(s) : Furstenberg,H. ; Katznelson,I. ; Shamir,E.

Report Date : APR 1971

Pagination or Media Count : 10

Abstract : The report describes problems belonging to classical Fourier analysis. These involve properties of certain Banach spaces of functions on the circle which are defined in terms of the Fourier series of the functions. Harmonic analysis is also used to sharpen a theorem in ergodic theory. The main result proved is that any ergodic automorphism of the torus is measure-theoretically isomorphic to a Bernoulli shift. This was known to be true under added conditions on the eigenvalues of the automorphism. The original methods depended heavily on the geometry of the torus and did not lend themselves to generalization to other compact abelian groups. The present method is more powerful and should generalize to other groups. The authors also use notions of ergodic theory as a tool in group theory. A group is studied in terms of the manner in which it can act on a compact space. These notions are useful in the theory of discrete subgroups of a Lie group. Finally, the authors consider the regularity of solutions to elliptic differential equations. (Author)

Descriptors :   (*HARMONIC ANALYSIS, THEOREMS), (*MEASURE THEORY, THEOREMS), FOURIER ANALYSIS, BANACH SPACE, GROUPS(MATHEMATICS), PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS, NUMERICAL INTEGRATION, TOPOLOGY, SERIES(MATHEMATICS), ISRAEL

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE