Investigations in Harmonic Analysis, Ergodic Theory and Related Topics in Analysis

"A number of problems in harmonic analysis as well as in some related domains of analysis are considered. These include problems arising in trying to extend classical harmonic analysis to non-commutative groups, as well as problems arising within the classical framework. (Author)."@en
"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)."@en

"Investigations in Harmonic Analysis, Ergodic Theory and Related Topics in Analysis"@en
"Investigations in harmonic analysis, ergodic theory, and related topics in analysis"@en