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Finite sections of band-dominated operators

Author: Steffen Roch
Publisher: Providence, R.I. : American Mathematical Society, 2008.
Series: Memoirs of the American Mathematical Society, no. 895.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Intends to review the advances and to present the results in the numerical analysis of the finite sections method for general band and band-dominated operators. This title addresses topics such as  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Steffen Roch
ISBN: 9780821840429 0821840428
OCLC Number: 173368776
Notes: "Volume 191, number 895 (end of volume)."
Description: vii, 87 pages : illustrations ; 26 cm.
Contents: Band-dominated operators --
Stability --
Fredholm band-dominated operators and their indices --
Algebras of matrix sequences --
Stability vs. Fredholmness --
Stability of the finite sections method --
Band-dominated operators with slowly oscillating coefficients --
The role of the index --
The C*-algebra of the finite sections method --
Another perspective on localization --
Stable regularizability --
Moore-Penrose invertibility in C*-algebras --
Stable regularizability vs. Moore-Penrose invertibility --
Stable regularizability of the finite sections method --
Compactness --
Compact sequences --
Characterization via singular values --
Central rank characterizations --
Minimal and maximal characterizations --
Compact sequences in S(N) and S(Z) --
Fredholmness --
Fredholm sequences --
Fredholmness and stability --
Fredholmness and stable regularizability --
Fredholmness of the finite sections method --
Slowly oscillating coefficients --
Essential fractality --
Fractality of quotient maps --
J-fractal algebras --
Essential fractality and singular values --
Essential fractality of the finite sections algebras --
Applications --
Approximation numbers --
Rank-preserving discretizations --
Arveson dichotomy: band-dominated operators --
Arveson dichotomy: the general setting --
Essential spectra --
Essential pseudospectra --
Pseudomodes --
Determinants.
Series Title: Memoirs of the American Mathematical Society, no. 895.
Responsibility: Steffen Roch.
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