Banach Algebras with Symbol and Singular Integral Operators by N. KrupnikBanach Algebras with Symbol and Singular Integral Operators by N. Krupnik

Banach Algebras with Symbol and Singular Integral Operators

byN. Krupnik

Paperback | April 11, 2014

Pricing and Purchase Info

$128.95

Earn 645 plum® points

Prices and offers may vary in store

Quantity:

In stock online

Ships free on orders over $25

Not available in stores

about

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.
Title:Banach Algebras with Symbol and Singular Integral OperatorsFormat:PaperbackPublished:April 11, 2014Publisher:Birkhäuser BaselLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:303485465X

ISBN - 13:9783034854658

Look for similar items by category:

Reviews