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Banach Algebras with Symbol and Singular Integral Operators (Paperback, Softcover reprint of the original 1st ed. 1987)
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Banach Algebras with Symbol and Singular Integral Operators (Paperback, Softcover reprint of the original 1st ed. 1987)
Series: Operator Theory: Advances and Applications, 26
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About fifty years aga S. G. Mikhlin, in solving the regularization
problem for two-dimensional singular integral operators [56],
assigned to each such operator a func tion which he called a
symbol, and showed that regularization is possible if the infimum
of the modulus of the symbol is positive. Later, the notion of a
symbol was extended to multidimensional singular integral operators
(of arbitrary dimension) [57, 58, 21, 22]. Subsequently, the
synthesis of singular integral, and differential operators [2, 8,
9]led to the theory of pseudodifferential operators [17, 35] (see
also [35(1)-35(17)]*), which are naturally characterized by their
symbols. An important role in the construction of symbols for many
classes of operators was played by Gelfand's theory of maximal
ideals of Banach algebras [201. Using this the ory, criteria were
obtained for Fredholmness of one-dimensional singular integral
operators with continuous coefficients [34 (42)], Wiener-Hopf
operators [37], and multidimensional singular integral operators
[38 (2)]. The investigation of systems of equations involving such
operators has led to the notion of matrix symbol [59, 12 (14), 39,
41]. This notion plays an essential role not only for systems, but
also for singular integral operators with piecewise-continuous
(scalar) coefficients [44 (4)]. At the same time, attempts to
introduce a (scalar or matrix) symbol for other algebras have
failed.
General
Imprint: |
Springer Basel
|
Country of origin: |
Switzerland |
Series: |
Operator Theory: Advances and Applications, 26 |
Release date: |
April 2014 |
First published: |
1987 |
Authors: |
N. Krupnik
|
Dimensions: |
244 x 170 x 12mm (L x W x T) |
Format: |
Paperback
|
Pages: |
206 |
Edition: |
Softcover reprint of the original 1st ed. 1987 |
ISBN-13: |
978-3-03-485465-8 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Algebra >
General
|
LSN: |
3-03-485465-X |
Barcode: |
9783034854658 |
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