In this volume three important papers of M.G. Krein appear for the first time in English translation. Each of them is a short self-contained monograph, each a masterpiece of exposition. Although two of them were writt...
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ISBN:
(数字)9783034854160
ISBN:
(纸本)9783034854184
In this volume three important papers of M.G. Krein appear for the first time in English translation. Each of them is a short self-contained monograph, each a masterpiece of exposition. Although two of them were written more than twenty years ago, the passage of time has not decreased their value. They are as fresh and vital as if they had been written only yesterday. These papers contain a wealth of ideas, and will serve as a source of stimulation and inspiration for experts and beginners alike. The first paper is dedicated to the theory of canonical linear differential equations, with periodic coefficients. It focuses on the study of linear Hamiltonian systems with bounded solutions which stay bounded under small perturbations of the system. The paper uses methods from operatortheory in finite and infinite dimensional spaces and complex analysis. For an account of more recent literature which was generated by this paper see AMS Translations (2), Volume 93, 1970, pages 103-176 and Integral Equations and operatortheory, Volume 5, Number 5, 1982, pages 718-757.
This volume presents the proceedings of the 11th Conference on Problems and Methods in Mathematical Physics (11th TMP), held in Chemnitz, March 25-28, 1999. The conference was dedicated to the memory of Siegfried Pr&#...
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ISBN:
(数字)9783034882767
ISBN:
(纸本)9783764364779;9783034895002
This volume presents the proceedings of the 11th Conference on Problems and Methods in Mathematical Physics (11th TMP), held in Chemnitz, March 25-28, 1999. The conference was dedicated to the memory of Siegfried Prössdorf, who made important contributions to the theory and numerical analysis of operator equations and their applications in mathematical physics and mechanics. The main part of the book comprises original research papers. The topics are ranging from integral and pseudodifferential equations, boundary value problems, operatortheory, boundary element and wavelet methods, approximation theory and inverse problems to various concrete problems and applications in physics and engineering, and reflect Prössdorf's broad spectrum of research activities. The volume also contains articles describing the life and mathematical achievements of Siegfried Prössdorf and includes a list of his publications. The book is addressed to a wide audience in the mathematical and engineering sciences.
This volume is dedicated to A.C. Zaanen, one of the pioneers of functional analysis, and eminent expert in modern integration theory and the theory of vector lattices, on the occasion of his 80th birthday. The book op...
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ISBN:
(数字)9783034890762
ISBN:
(纸本)9783034898966
This volume is dedicated to A.C. Zaanen, one of the pioneers of functional analysis, and eminent expert in modern integration theory and the theory of vector lattices, on the occasion of his 80th birthday. The book opens with biographical notes, including Zaanen's curriculum vitae and list of publications. It contains a selection of original research papers which cover a broad spectrum of topics about operators and semigroups of operators on Banach lattices, analysis in function spaces and integration theory. Special attention is paid to the spectral theory of operators on Banach lattices; in particular, to the one of positive operators. Classes of integral operators arising in systems theory, optimization and best approximation problems, and evolution equations are also discussed. The book will appeal to a wide range of readers engaged in pure and applied mathematics.
This monograph presents necessary and sufficient conditions for completeness of the linear span of eigenvectors and generalized eigenvectors of operators that admit a characteristic matrix function in a Banach space s...
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ISBN:
(数字)9783031045080
ISBN:
(纸本)9783031045073;9783031045103
This monograph presents necessary and sufficient conditions for completeness of the linear span of eigenvectors and generalized eigenvectors of operators that admit a characteristic matrix function in a Banach space setting. Classical conditions for completeness based on the theory of entire functions are further developed for this specific class of operators. The classes of bounded operators that are investigated include trace class and Hilbert-Schmidt operators, finite rank perturbations of Volterra operators, infinite Leslie operators, discrete semi-separable operators, integral operators with semi-separable kernels, and period maps corresponding to delay differential equations. The classes of unbounded operators that are investigated appear in a natural way in the study of infinite dimensional dynamical systems such as mixed type functional differential equations, age-dependent population dynamics, and in the analysis of the Markov semigroup connected to the recently introduced zig-zag process.
This volume is dedicated to Tsuyoshi Ando, a foremost expert in operatortheory, matrix theory, complex analysis, and their applications, on the occasion of his 60th birthday. The book opens with his biography and lis...
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ISBN:
(数字)9783034885812
ISBN:
(纸本)9783764329280;9783034896900
This volume is dedicated to Tsuyoshi Ando, a foremost expert in operatortheory, matrix theory, complex analysis, and their applications, on the occasion of his 60th birthday. The book opens with his biography and list of publications. It contains a selection of papers covering a broad spectrum of topics ranging from abstract operatortheory to various concrete problems and applications. The majority of the papers deal with topics in modern operatortheory and its applications. This volume also contains papers on interpolation and completion problems, factorization problems and problems connected with complex analysis. The book will appeal to a wide audience of pure and applied mathematicians.
This two-volume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The main attention is paid to fast algorithms (many of linear complexity) for m...
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ISBN:
(数字)9783034806060
ISBN:
(纸本)9783034806053
This two-volume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The main attention is paid to fast algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and companion form. The work is focused on algorithms of multiplication, inversion and description of eigenstructure and includes a large number of illustrative examples throughout the different chapters. The first volume consists of four parts. The first part is of a mainly theoretical character introducing and studying the quasiseparable and semiseparable representations of matrices and minimal rank completion problems. Three further completions are treated in the second part. The first applications of the quasiseparable and semiseparable structure are included in the third part where the interplay between the quasiseparable structure and discrete time varying linear systems with boundary conditions play an essential role. The fourth part contains factorization and inversion fast algorithms for matrices via quasiseparable and semiseparable structure. The work is based mostly on results obtained by the authors and their coauthors. Due to its many significant applications and the accessible style the text will be useful to engineers, scientists, numerical analysts, computer scientists and mathematicians alike.
Noncommutative geometry, which can rightfully claim the role of a philosophy in mathematicalstudies,undertakesto replacegoodoldnotionsofclassicalgeometry (suchas manifolds,vectorbundles, metrics, di?erentiable structu...
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ISBN:
(数字)9783764387754
ISBN:
(纸本)9783764387747
Noncommutative geometry, which can rightfully claim the role of a philosophy in mathematicalstudies,undertakesto replacegoodoldnotionsofclassicalgeometry (suchas manifolds,vectorbundles, metrics, di?erentiable structures,etc. ) by their abstract operator-algebraic analogs and then to study the latter by methods of the theory of operator algebras. At ?rst sight, this pursuit of maximum possible generality harbors the danger of completely forgetting the classical beginnings, so that not only the answers but also the questions would defy stating in traditional terms. Noncommutative geometry itself would become not only a method but also the main subject of investigation according to the capacious but not too practical formula: “Know thyself. ” Fortunately, this is not completely true (or even is completely untrue) in reality: there are numerous problems that are quite classical in their statement (or at least admit an equivalent classical statement) but can be solved only in the framework of noncommutative geometry. One of such problems is the subject of the present book. The classical elliptic theory developed in the well-known work of Atiyah and Singer on the index problem relates an analytic invariant of an elliptic pseud- i?erential operator on a smooth compact manifold, namely, its index, to topol- ical invariants of the manifold itself. The index problem for nonlocal (and hence nonpseudodi?erential) elliptic operators is much more complicated and requires the use of substantially more powerful methods than those used in the classical case.
This is a collection of contributed papers which focus on recent results in areas of differential equations, function spaces, operatortheory and interpolation theory. In particular, it covers current w...
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ISBN:
(数字)9783034802635
ISBN:
(纸本)9783034802628;9783034807609
This is a collection of contributed papers which focus on recent results in areas of differential equations, function spaces, operatortheory and interpolation theory. In particular, it covers current work on measures of non-compactness and real interpolation, sharp Hardy-Littlewood-Sobolev inequalites, the HELP inequality, error estimates and spectral theory of elliptic operators, pseudo differential operators with discontinuous symbols, variable exponent spaces and entropy numbers. These papers contribute to areas of analysis which have been and continue to be heavily influenced by the leading British analysts David Edmunds and Des Evans. This book marks their respective 80th and 70th birthdays.
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