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Partial Differential Equations VIII: Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory: 65 (Encyclopaedia of Mathematical Sciences, 65) - Softcover
Synopsis
Consider a linear partial differential operator A that maps a vector-valued function Y = (Yl,"" Ym) into a vector-valued function I = (h,···, II). We assume at first that all the functions, as well as the coefficients of the differen tial operator, are defined in an open domain Jl in the n-dimensional Euclidean n space IR , and that they are smooth (infinitely differentiable). A is called an overdetermined operator if there is a non-zero differential operator A' such that the composition A' A is the zero operator (and underdetermined if there is a non-zero operator A" such that AA" = 0). If A is overdetermined, then A'I = 0 is a necessary condition for the solvability of the system Ay = I with an unknown vector-valued function y. 3 A simple example in 1R is the operator grad, which maps a scalar func tion Y into the vector-valued function (8y/8x!, 8y/8x2, 8y/8x3)' A necessary solvability condition for the system grad y = I has the form curl I = O.
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From the Back Cover
This volume of the EMS contains three articles, on linear overdetermined systems of partial differential equations, dissipative Schroedinger operators, and index theorems. Each article presents a comprehensive survey of its subject, discussing fundamental results such as the construction of compatibility operators and complexes for elliptic, parabolic and hyperbolic coercive problems, the method of functional models and the Atiyah-Singer index theorem and its generalisations. Both classical and recent results are explained in detail and illustrated by means of examples.
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- PublisherSpringer
- Publication date2012
- ISBN 10 364248946X
- ISBN 13 9783642489464
- BindingPaperback
- LanguageEnglish
- Number of pages268
- EditorShubin M.A.
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Partial Differential Equations VIII: Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory (Encyclopaedia of Mathematical Sciences)
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Partial Differential Equations VIII
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This volume of the EMS contains three articles, on linear overdetermined systems of partial differential equations, dissipative Schroedinger operators, and index theorems. Each article presents a comprehensive survey of its subject, discussing fundamental results such as the construction of compatibility operators and complexes for elliptic, parabolic and hyperbolic coercive problems, the method of functional models and the Atiyah-Singer index theorem and its generalisations. Both classical and recent results are explained in detail and illustrated by means of examples. 272 pp. Englisch. Seller Inventory # 9783642489464
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Partial Differential Equations VIII
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. I. Linear Overdetermined Systems of Partial Differential Equations. Initial and Initial-Boundary Value Problems.- II. Spectral Analysis of a Dissipative Singular Schroedinger Operator in Terms of a Functional Model.- III. Index Theorems.- Author Index. Seller Inventory # 5062472
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Partial Differential Equations VIII : Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This volume of the EMS contains three articles, on linear overdetermined systems of partial differential equations, dissipative Schroedinger operators, and index theorems. Each article presents a comprehensive survey of its subject, discussing fundamental results such as the construction of compatibility operators and complexes for elliptic, parabolic and hyperbolic coercive problems, the method of functional models and the Atiyah-Singer index theorem and its generalisations. Both classical and recent results are explained in detail and illustrated by means of examples. Seller Inventory # 9783642489464
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Partial Differential Equations VIII: Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory (Encyclopaedia of Mathematical Sciences)
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Partial Differential Equations VIII
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Taschenbuch. Condition: Neu. Neuware -Consider a linear partial differential operator A that maps a vector-valued function Y = (Yl,'' Ym) into a vector-valued function I = (h, , II). We assume at first that all the functions, as well as the coefficients of the differen tial operator, are defined in an open domain Jl in the n-dimensional Euclidean n space IR , and that they are smooth (infinitely differentiable). A is called an overdetermined operator if there is a non-zero differential operator A' such that the composition A' A is the zero operator (and underdetermined if there is a non-zero operator A' such that AA' = 0). If A is overdetermined, then A'I = 0 is a necessary condition for the solvability of the system Ay = I with an unknown vector-valued function y. 3 A simple example in 1R is the operator grad, which maps a scalar func tion Y into the vector-valued function (8y/8x!, 8y/8x2, 8y/8x3)' A necessary solvability condition for the system grad y = I has the form curl I = O.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 272 pp. Englisch. Seller Inventory # 9783642489464
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Partial Differential Equations VIII: Overdetermined Systems Dissipative Singular Schr Dinger Operator Index Theory (Encyclopaedia of Mathematical Sciences)
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Partial Differential Equations VIII: Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory (Encyclopaedia of Mathematical Sciences)
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