Author | Rabinovich, Vladimir. author |
---|---|
Title | Limit Operators and Their Applications in Operator Theory [electronic resource] / by Vladimir Rabinovich, Bernd Silbermann, Steffen Roch |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2004 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-7911-8 |
Descript | XV, 392 p. online resource |
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 $${L̂p}\left( {{\mathbb{R}̂N}} \right)$$ -- 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 $${L̂2}\left( {{\mathbb{R}̂N}} \right)$$ -- 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 Schrรถdinger operators -- 5.9 Comments and references -- 6 Finite Sections of Band-dominated Operators -- 6.1 Stability of the finite section method -- 6.2 Finite 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