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Titlebook: Classes of Linear Operators; Israel Gohberg,Marinus A. Kaashoek,Seymour Goldber Book 1993 Birkhäuser Verlag 1993 Mathematik.complex analys

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书目名称Classes of Linear Operators
编辑Israel Gohberg,Marinus A. Kaashoek,Seymour Goldber
视频video
丛书名称Operator Theory: Advances and Applications
图书封面Titlebook: Classes of Linear Operators;  Israel Gohberg,Marinus A. Kaashoek,Seymour Goldber Book 1993 Birkhäuser Verlag 1993 Mathematik.complex analys
描述These two volumes constitute texts for graduate courses in linear operator theory. The reader is assumed to have a knowledge of both complex analysis and the first elements of operator theory. The texts are intended to concisely present a variety of classes of linear operators, each with its own character, theory, techniques and tools. For each of the classes, various differential and integral operators motivate or illustrate the main results. Although each class is treated seperately and the first impression may be that of many different theories, interconnections appear frequently and unexpectedly. The result is a beautiful, unified and powerful theory. The classes we have chosen are representatives of the principal important classes of operators, and we believe that these illustrate the richness of operator theory, both in its theoretical developments and in its applicants. Because we wanted the books to be of reasonable size, we were selective in the classes we chose and restricted our attention to the main features of the corresponding theories. However, these theories have been updated and enhanced by new developments, many of which appear here for the first time in an operat
出版日期Book 1993
关键词Mathematik; complex analysis; functional analysis; science; spectral theory
版次1
doihttps://doi.org/10.1007/978-3-0348-8558-4
isbn_softcover978-3-0348-9679-5
isbn_ebook978-3-0348-8558-4Series ISSN 0255-0156 Series E-ISSN 2296-4878
issn_series 0255-0156
copyrightBirkhäuser Verlag 1993
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Robbert van Renesse,Rachid Guerraouitation to construct explicitly the factors in a canonical Wiener-Hopf factorization. This yields explicit formulas for the inverse and the Fredholm characteristics. The results obtained here may be viewed as discrete analogues of the inversion and Fredholm theorems for Wiener-Hopf integral operators in Chapter XIII.
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https://doi.org/10.1007/b101825 are identified as pure isometries. In the second section it is shown that block backward shifts provide universal models for arbitrary operators. The third section describes the invariant subspaces of ℂ.-block forward shifts. Throughout this chapter all operators are Hilbert space operators.
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Multiplicative Lower-Upper Triangular Decompositions of Operatorst, under certain conditions, a matrix can be represented as a product of a lower with an upper triangular matrix. Also, the possibility of factoring certain integral operators as the product of integral operators with lower and upper triangular kernel functions is treated as a special case of the general theory which we now develop.
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Toeplitz Operators Defined by Rational Matrix Functionstation to construct explicitly the factors in a canonical Wiener-Hopf factorization. This yields explicit formulas for the inverse and the Fredholm characteristics. The results obtained here may be viewed as discrete analogues of the inversion and Fredholm theorems for Wiener-Hopf integral operators in Chapter XIII.
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Palgrave Macmillan Memory Studiesough each class is treated seperately and the first impression maybe that ofmany different theories, interconnections appear frequently and expectedly. The result is a beautiful, unified and powerful theory.
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