
Banach Algebras with Symbol and Singular Integral Operators
N. Krupnik(Author)
Birkhäuser (Publisher)
Published on 11. April 2014
Book
Paperback/Softback
X, 206 pages
978-3-0348-5465-8 (ISBN)
Description
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.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1987
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
X, 206 p.
Dimensions
Height: 244 mm
Width: 170 mm
Thickness: 13 mm
Weight
389 gr
ISBN-13
978-3-0348-5465-8 (9783034854658)
DOI
10.1007/978-3-0348-5463-4
Schweitzer Classification
Other editions
Additional editions
Naum Y. Krupnik | Izrael Gohberg
Banach Algebras with Symbol and Singular Integral Operators
Book
01/1987
Birkhäuser Verlag GmbH
€98.00
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