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Project
Quasianalytic and non-quasianalytic classes in Fourier analysis and approximation theory
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.
Date:1 Jan 2014 → 31 Oct 2018
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.
Disciplines:Analysis, Functional analysis, Several complex variables and analytic spaces, Integral transforms, operational calculus, Operator theory, Functions of a complex variable, Partial differential equations, Approximations and expansions, Harmonic analysis on Euclidean spaces