Accession Number : AD0678201

Title :   SPECIAL PROGRAM IN MATHEMATICAL ANALYSIS.

Descriptive Note : Final scientific status rept.,

Corporate Author : INSTITUTE FOR ADVANCED STUDY PRINCETON N J

Personal Author(s) : Beurling,Arne

Report Date : 18 SEP 1968

Pagination or Media Count : 4

Abstract : The research carried out belonged mainly to the following fields: (1) Harmonic analysis on abelian groups and analytic functions of one or several complex variables: Distribution of generalized primes and the connected Dirichlet divisor problem (Diamond). The density problem for balayage (Landau). Closure properties of given sets of characters (Malliavin and Beurling). Analytic functions of several complex variables (Narasimhan, partly with Borel, Gunning). The monodromy theorem (Ryff). Extension to analytic modules of a theorem of Osgood and Hartogs (Spallek). Harmonic analysis on local fields (Taibleson). (2) Harmonic analysis and group representations: The Plancherel theorem for solvable Lie groups (Brezin). The two-by-two unimodular group over a local field (Sally). (3) Functional analysis, differential operators: The closed graph theorem, bilinear forms in Hilbert space (McIntosh). Analytic approach to the Atiyah-Singer index theorem (Cohen). The lacunas in the solution of the wave equation (Garding). Cauchy problems (Goldstein). (Author)

Descriptors :   (*HARMONIC ANALYSIS, *GROUPS(MATHEMATICS)), (*FUNCTIONAL ANALYSIS, *OPERATORS(MATHEMATICS)), SET THEORY, DIFFERENTIAL EQUATIONS, ANALYTIC FUNCTIONS, HILBERT SPACE

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE