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

01 January 2014 → 31 October 2018
Regional and community funding: Special Research Fund
Research disciplines
  • Natural sciences
    • Analysis
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.