Regularity properties and generalized inverses of delta-related operators
type: Item
instance of: scholarly article
title: Regularity properties and generalized inverses of delta-related operators
zbMATH Open document ID: 0918.47026
DOI: 10.4171/ZAA/840
author: Frank-Olme Speck
author: L. P. Castro
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1998-10-14T00:00:00Z
review text: Summary: As a central topic certain relations between operator matrices are investigated which are called delta relations. The main aim of these relations is to reduce questions about classes of operators without invertibility symbol to those which admit an invertibility symbol. Particular attention is devoted to the generalized inversion of such operators. Different kinds of relations are introduced in order to analyze the ``information'' contained in the symbols of the related operators. Several examples are considered and the theory is also applied to singular integral operators with Carleman shift. Asymptotic solutions of equations characterized by those operators are presented. The approach simplifies several known results, makes the theory more rigorous from the operator theoretic point of view, and allows further conclusions in a very compact form.
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47A68
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 45F15
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 47G10
zbMATH DE Number: 1211542
zbMATH Keywords: delta-related operators
zbMATH Keywords: factorization theory
zbMATH Keywords: generalized inverses
zbMATH Keywords: relations between operator matrices
zbMATH Keywords: delta relations
zbMATH Keywords: invertibility symbol
zbMATH Keywords: generalized inversion
zbMATH Keywords: singular integral operators with Carleman shift
MaRDI profile type: Publication
cites work: Minimal factorization of matrix and operator functions
cites work: Q4287397
cites work: Complementary Schur complements
cites work: Q4040771
cites work: Meromorphic Factorization, Partial Index Estimates and Elastodynamic Diffraction Problems1)
cites work: Q4394658
cites work: On the Characterization of the Intermediate Space in Generalized Factorizations
cites work: On the inversion of higher order Wiener-Hopf operators
cites work: Q4515696
cites work: Q4776369
cites work: Q4301589
cites work: Fredholm Theory for a Class of Singular Integral Operators with Carleman Shift and Unbounded Coefficients
cites work: Banach algebras with symbol and singular integral operators. Transl. from the Russian by A. Iacob
cites work: Some results on the invertibility of Wiener-Hopf-Hankel operators
cites work: Q3031337
cites work: Wiener-Hopf-Hankel operators for some wedge diffraction problems with mixed boundary conditions
cites work: Some interior and exterior boundary-value problems for the Helmholtz equation in a quadrant
cites work: Two canonical wedge problems for the Helmholtz equation
cites work: Q3752967
cites work: Q3821119
cites work: Q4282408
cites work: Q3715553
cites work: Least Squares Approximate and Least Norm Solutions of Paired Singular Equations
cites work: On a class of Hankel operators: Fredholm properties and invertibility
cites work: Diffraction by a rectangular wedge: Wiener-Hopf-Hankel formulation
cites work: Q4169289
full work available at URL: https://doi.org/10.4171/zaa/840
OpenAlex ID: W2021606415
description: scientific article; zbMATH DE number 1211542