Vladimir Rabinovich, Steffen Roch, Bernd Silbermann

Limit Operators and Their Applications in Operator Theory (eBook, PDF)

• Format: PDF

Produktbeschreibung

The book is devoted to a class of operators which occurs in almost every part of mathematics: band and band-dominated operators on spaces of vector-valued sequences. The main emphasis is on Fredholm theory for these operators, and the main tool to study this topic is the method of limit operators. Applications are presented to several important classes of such operators: convolution type operators, pseudodifferential and pseudodifference operators.

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Produktdetails

• Verlag: Springer Basel
• Seitenzahl: 392
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783034879118
• Artikelnr.: 53086272

Autorenporträt

Vladimir Rabinovich, National Politechnic Institute of Mexico, Mexico

Inhaltsangabe

1 Limit Operators.- 1.1 Generalized compactness, generalized convergence.- 1.2 Limit operators.- 1.3 Algebraization.- 1.4 Comments and references.- 2 Fredholmness of Band-dominated Operators.- 2.1 Band-dominated operators.- 2.2 P-Fredholmness of rich band-dominated operators.- 2.3 Local P-Fredholmness: elementary theory.- 2.4 Local P-Fredholmness: advanced theory.- 2.5 Operators in the discrete Wiener algebra.- 2.6 Band-dominated operators with special coefficients.- 2.7 Indices of Fredholm band-dominated operators.- 2.8 Comments and references.- 3 Convolution Type Operators on $${mathbb{R}^N}$$.- 3.1 Band-dominated operators on $${L^p}left( {{mathbb{R}^N}} right)$$.- 3.2 Operators of convolution.- 3.3 Fredholmness of convolution type operators.- 3.4 Compressions of convolution type operators.- 3.5 A Wiener algebra of convolution-type operators.- 3.6 Comments and references.- 4 Pseudodifferential Operators.- 4.1 Generalities and notation.- 4.2 Bi-discretization of operators on $${L^2}left( {{mathbb{R}^N}} right)$$.- 4.3 Fredholmness of pseudodifferential operators.- 4.4 Applications.- 4.5 Mellin pseudodifferential operators.- 4.6 Singular integrals over Carleson curves with Muckenhoupt weights.- 4.7 Comments and references.- 5 Pseudodifference Operators.- 5.1 Pseudodifference operators.- 5.2 Fredholmness of pseudodifference operators.- 5.3 Fredholm properties of pseudodifference operators on weighted spaces.- 5.4 Slowly oscillating pseudodifference operators.- 5.5 Almost periodic pseudodifference operators.- 5.6 Periodic pseudodifference operators.- 5.7 Semi-periodic pseudodifference operators.- 5.8 Discrete Schrödinger operators.- 5.9 Comments and references.- 6 Finite Sections of Band-dominated Operators.- 6.1 Stability of the finite section method.- 6.2Finite sections of band-dominated operators on $${mathbb{Z}^1}$$ and $${mathbb{Z}^2}$$.- 6.3 Spectral approximation.- 6.4 Fractality of approximation methods.- 6.5 Comments and references.- 7 Axiomatization of the Limit Operators Approach.- 7.1 An axiomatic approach to the limit operators method.- 7.2 Operators on homogeneous groups.- 7.3 Fredholm criteria for convolution type operators with shift.- 7.4 Comments and references.