Project

Quasianalytic and non-quasianalytic classes in Fourier analysis and approximation theory

Code
01N01014
Duration
01 January 2014 → 31 October 2018
Funding
Regional and community funding: Special Research Fund
Research disciplines
  • Natural sciences
    • Approximations and expansions
    • Functional analysis
    • Functions of a complex variable
    • Harmonic analysis on Euclidean spaces
    • Integral transforms, operational calculus
    • Operator theory
    • Partial differential equations
    • Several complex variables and analytic spaces
Keywords
Convolution algebras Spectral synthesis Tauberian theory Elliptic pseudo-differential operators Fréchet algebras ultradifferentialble functions Spectral expansions Approximation theory generalized Fourier series expansions Quasianalyticity fourier analysis ultradistributions.
 
Project description

The first part of the project investigates spaces of ultra-differentiable functions in terms of the growth of Fourier coefficients compared to spectral developments related to elliptical pseudo-differential operators. The second part deals with significant extensions of the famous theorem of Beurling-Wiener for convolutional algebras and applications in the Taubian theory of the asymptotics of integral transformations for large values of the parameter.