Overdetermined systems, dissipative singular Schrödinger operator, index theory
著者
書誌事項
Overdetermined systems, dissipative singular Schrödinger operator, index theory
（Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze, v. 65 . Partial differential equations ; 8）
Springer-Verlag, c1996
- : gw
- : us
- :pbk
- タイトル別名
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Differentsial'nye uravneniya s chastnymi proizvodnymi
Different︠s︡ialʹnye uravnenii︠a︡ s chastnymi proizvodnymi
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注記
Translation of: "Different︠s︡ialńye uravnenii︠a︡ s chastnymi proizvodnymi 8," which is vol.65 of the serial "Itogi nauki i tekhniki, Sovremennye problemy matematiki, Fundamentalńye napravlenii︠a︡"
Includes bibliographical references, author and subject indexes
内容説明・目次
- 巻冊次
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: gw ISBN 9783540570363
内容説明
This volume contains three articles on linear overdetermined systems of partial differential equations, dissipative Schroedinger operators, and index theorems. Each article presents a 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 generalizations. Both classical and recent results are explained in detail and illustrated by means of example.
目次
I. Linear Overdetermined Systems of Partial Differential Equations. Initial and Initial-Boundary Value Problems.- II. Spectral Analysis of a Dissipative Singular Schrodinger Operator in Terms of a Functional Model.- III. Index Theorems.- Author Index.
- 巻冊次
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:pbk ISBN 9783642489464
内容説明
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.
目次
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.
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