Memory Estimation of Inverse Operators

Abstract

We use methods of harmonic analysis and group rep- resentation theory to estimate memory decay of the inverse oper- ators in Banach spaces. The memory of the operators is defined using the notion of the Beurling spectrum. We obtain a general continuous non-commutative version of the celebrated Wiener's Tauberian lemma with estimates of the "Fourier coefficients" of inverse operators. In particular, we generalize various estimates of the elements of the inverse matrices. The results are illus- trated with a variety of examples including integral and integro- differential operators.

52 pages

References in corpus (2)

• Inverse-Closedness of a Banach Algebra of Integral Operators on the Heisenberg Group
• Spectral Invariance of Besov-Bessel Subalgebras

Cited by in corpus (6)

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• Kadec-type theorems for sampled group orbits
• Inverse-closedness of subalgebras of integral operators with almost periodic kernels
• Stability of Localized Integral Operators on Weighted $L^p$ spaces
• Polynomial control on stability, inversion and powers of matrices on simple graphs