Memory Estimation of Inverse Operators

Details Memory Estimation of Inverse Operators Memory Estimation of Inverse Operators

2011-03-14

arxiv.org/abs/1103.2748v1

Mathematics

Functional Analysis

52 pages

Scientific paper

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.

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