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Partial Differential Equations VIII: Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory: 65 (Encyclopaedia of Mathematical Sciences) - Tapa blanda
Sinopsis
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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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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Partial Differential Equations VIII: Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory (Encyclopaedia of Mathematical Sciences)
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Partial Differential Equations VIII : Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory
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Partial Differential Equations VIII (Paperback)
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Paperback. Condición: new. Paperback. 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. This volume 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Nº de ref. del artículo: 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 : Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory
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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: Overdetermined Systems Dissipative Singular Schrödinger Operator Index Theory (Encyclopaedia of Mathematical Sciences)
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Partial Differential Equations VIII
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Springer Berlin Heidelberg Apr 2012, 2012
ISBN 10: 364248946X
ISBN 13: 9783642489464
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Taschenbuch. Condición: 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. Nº de ref. del artículo: 9783642489464
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Partial Differential Equations VIII
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Springer Berlin Heidelberg, 2012
ISBN 10: 364248946X
ISBN 13: 9783642489464
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Condición: 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. Nº de ref. del artículo: 5062472
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Partial Differential Equations
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Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 2012
ISBN 10: 364248946X
ISBN 13: 9783642489464
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Condición: New. Editor(s): Shubin, M.A. Translator(s): Constanda, Christian. Series: Encyclopaedia of Mathematical Sciences. Num Pages: 268 pages, biography. BIC Classification: PBK; PBMW; PHU. Category: (P) Professional & Vocational. Dimension: 234 x 156 x 14. Weight in Grams: 416. . 2012. Softcover reprint of the original 1st ed. 1996. Paperback. . . . . Nº de ref. del artículo: V9783642489464
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