Norm controlled inversion in l^1(Z)

16.12.2020 14:00 - 15:00

Stefan Egger (University of Vienna)

This talk is devoted to the question of how to estimate the norm of inverse elements a^{-1} in terms of a in l^1(Z). Taking a bare bound on the norm of a does not bound the norm of a^{-1}. Our approach will be to additionally put a norm constraint on the induced function obtained using Fourier transform of a^{-1}. We will show that in general even this does not suffice to bound the norm of a^{-1}: If we choose the bound on the function too large, bounding the norm of a^{-1} will again be not possible.

Presentation of part of the article:

El-Fallah O., Nikolski N. K., and Zarrabi M., Resolvent estimates in Beurling-Sobolev algebras, Algebra i Analiz, 6 (1998), 1–80.


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J. L. Romero, M. Ehler