Memory estimation of inverse operators

Abstract

We use methods of harmonic analysis and group representation theory to estimate memory decay of the inverse operators 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 illustrated with a variety of examples including integral and integrodifferential operators.

Multi-window Gabor frames in amalgam spaces

“…This means that if an operator from that algebra is invertible on L p , then the inverse operator necessarily belongs to the algebra. This approach is now common in timefrequency analysis [31,1,4,5,6,7,11,15,20,24,26,27] but its application to spaces that are not characterized by time-frequency decay is rather subtle. As a by-product, we obtain consequences that are new even for the case of one generator.…”

Оценки Функции Грина И Параметров Экспоненциальной Дихотомии Гиперболической Полугруппы Операторов И Линейных Отношений

“…Если оператор A принадлежит алгебре End X , то A ∈ End ℓ p , p ∈ [1, ∞], и для оценки функции Грина G : Z → End X можно использовать результаты статей [43]- [47] об оценках элементов обратных матриц для ограниченных операторов (см. также [48]).…”

Localization of Matrix Factorizations

“…Theorem 3.4. Assume that A is a strongly decomposable inverse closed subalgebra of B(ℓ 2 ) that satisfies conditions (7) and (8). Then any matrix A ∈ A that satisfies A − I B(ℓ 2 ) < 1 admits an LU-factorization A = LU in A such that…”

“…Yet another example of a useful functional calculus is in some sense a generalization of the approach in the Laurent case. Given A ∈ B c and h ∈ L 1 (R), we can define a Banach L 1 (R)-module structure [9] via This structure extends to a closed operator calculus as in [8]. Again, we have hA ∈ A as long as A is in a Banach algebra A that is invariant under the modulation representation.…”