Systems, Approximation, Singular Integral Operators, and Related Topics, Alexander A. Borichev; Nikolai K. Nikolski

Автор: A. B?ttcher; Solomon G. Mikhlin; R. Lehmann; Siegf
Название: Singular Integral Operators
ISBN: 3540159673 ISBN-13(EAN): 9783540159674
Издательство: Springer
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Описание: The present edition differs from the original German one mainly in the following addi- tional material: weighted norm inequalities for maximal functions and singular opera- tors ( 12, Chap. XII), and spline approximation methods for solving singular integral equations ( 4, Chap.

Автор: I. Gohberg; N. Krupnik
Название: One-Dimensional Linear Singular Integral Equations
ISBN: 3034897146 ISBN-13(EAN): 9783034897143
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Описание: This book is an introduction to the theory of linear one-dimensional singular integral equations. Singular integral equations have attracted more and more attention, because, on one hand, this class of equations appears in many applications and, on the other, it is one of a few classes of equations which can be solved in explicit form.

Автор: Estelle L. Basor; I. Gohberg
Название: Toeplitz Operators and Related Topics
ISBN: 3034896727 ISBN-13(EAN): 9783034896726
Издательство: Springer
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Описание: This volume is dedicated to Harold Widom, a distinguished mathematician and renowned expert in the area of Toeplitz, Wiener-Hopf and pseudodifferential operators, on the occasion of his sixtieth birthday. The book opens with biographical material and a list of the mathematician's publications, this being followed by two papers based on Toeplitz lectures which he delivered at Tel Aviv University in March, 1993. The rest of the book consists of a selection of papers containing some recent achievements in the following areas: Szego-Widom asymptotic formulas for determinants of finite sections of Toeplitz matrices and their generalizations, the Fisher-Hartwig conjecture, random matrices, analysis of kernels of Toeplitz matrices, projectional methods and eigenvalue distribution for Toeplitz matrices, the Fredholm theory for convolution type operators, the Nehari interpolation problem with generalizations and applications, and Toeplitz-Hausdorff type theorems. The book will appeal to a wide audience of pure and applied mathematicians.

Автор: A. Feintuch; I. Gohberg
Название: Nonselfadjoint Operators and Related Topics
ISBN: 3034896638 ISBN-13(EAN): 9783034896634
Издательство: Springer
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Описание: Our goal is to find Grabner bases for polynomials in four different sets of expressions: 1 x-, (1 - x)-1 (RESOL) X, 1 x- (1 - xy)-1 (EB) X, y-1, (1-yx)-1 y, (1_y)-1 (1-x)-1 (preNF) (EB) plus and (1 - xy)1/2 (1 - yx )1/2 (NF) (preNF) plus and Most formulas in the theory of the Nagy-Foias operator model NF] are polynomials in these expressions where x = T and y = T*. Complicated polynomials can often be simplified by applying "replacement rules". For example, the polynomial (1 - xy)-2 - 2xy(1-xy)-2 + xy2 (1 - xy)-2 -1 simplifies to O. This can be seen by three applications of the replacement rule (1-xy) -1 xy -t (1 - xy)-1 -1 which is true because of the definition of (1-xy)-1. A replacement rule consists of a left hand side (LHS) and a right hand side (RHS). The LHS will always be a monomial. The RHS will be a polynomial whose terms are "simpler" (in a sense to be made precise) than the LHS. An expression is reduced by repeatedly replacing any occurrence of a LHS by the corresponding RHS. The monomials will be well-ordered, so the reduction procedure will terminate after finitely many steps. Our aim is to provide a list of substitution rules for the classes of expressions above. These rules, when implemented on a computer, provide an efficient automatic simplification process. We discuss and define the ordering on monomials later.

Автор: Victor P. Havin; Nikolai K. Nikolski
Название: Complex Analysis, Operators, and Related Topics
ISBN: 3034895410 ISBN-13(EAN): 9783034895415
Издательство: Springer
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Описание: This volume is devoted to some topical problems and various applications of operator theory and its interplay with modern complex analysis. 30 carefully selected surveys and research papers are united by the "operator theoretic ideology" and systematic use of modern function theoretical techniques.

Автор: M.A. Krasnosel`skii; P.P. Zabreyko; E.I. Pustylnik
Название: Integral operators in spaces of summable functions
ISBN: 9401015449 ISBN-13(EAN): 9789401015448
Издательство: Springer
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Описание: The investigation of many mathematical problems is significantly simplified if it is possible to reduce them to equations involving continuous or com- pletely continuous operators in function spaces.

Автор: Vakhtang Kokilashvili; Alexander Meskhi; Humberto
Название: Integral Operators in Non-Standard Function Spaces
ISBN: 3319210173 ISBN-13(EAN): 9783319210179
Издательство: Springer
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Описание: This book, the result of the authors' long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Holder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them.

The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book's most distinctive features is that the majority of the statements proved here are in the form of criteria.

The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.

Автор: Kokilashvili, Vakhtang Meskhi, Alexander Samko, Stefan (faculdade De Ciencias E Tecnologia, Universidade Do Algarve, Faro, Portugal)
Название: Integral operators in non-standard function spaces
ISBN: 3319210149 ISBN-13(EAN): 9783319210148
Издательство: Springer
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Описание: Preface.- I: Variable Exponent Lebesgue and Amalgam spaces.- 1 Hardy Type Operators.- 2 Oscillating weights.- 3 Kernel Integral Operators.- 4 Two-Weight Estimates.- 5 One-sided Operators.- 6 Two-weight Inequalities for Fractional Maximal Functions.- 7 Hypersingular Integrals.- 8 Description of the Range of Potentials 213.- 9 More on Compactness.- 10 Applications to Singular Integral Equations.- II: Hцlder Spaces of Variable Order.- 11 Variable Order Hцlder Spaces.- III: Variable Exponent Morrey-Campanato and Herz Spaces.- 12 Morrey Type Spaces; Constant Exponents.- 13 Morrey Type Spaces; Variable Exponents.- Bibliography.- Symbol Index.- Subject Index.