Banach Algebras with Symbol and Singular Integral Operators is popular PDF and ePub book, written by N. Krupnik in 2013-11-22, it is a fantastic choice for those who relish reading online the Science genre. Let's immerse ourselves in this engaging Science book by exploring the summary and details provided below. Remember, Banach Algebras with Symbol and Singular Integral Operators can be Read Online from any device for your convenience.
Banach Algebras with Symbol and Singular Integral Operators Book PDF Summary
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.
Detail Book of Banach Algebras with Symbol and Singular Integral Operators PDF
- Author : N. Krupnik
- Release : 22 November 2013
- Publisher : Birkhäuser
- ISBN : 9783034854634
- Genre : Science
- Total Page : 212 pages
- Language : English
- PDF File Size : 7,9 Mb
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