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Home > Mathematics and Science books > Mathematics > Calculus and mathematical analysis > Differential calculus and equations > Differential Equations on Singular Manifolds: Semiclassical Theory and Operator Algebras(Mathematical Topics S.)
Differential Equations on Singular Manifolds: Semiclassical Theory and Operator Algebras(Mathematical Topics S.)

Differential Equations on Singular Manifolds: Semiclassical Theory and Operator Algebras(Mathematical Topics S.)


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About the Book

In the book, new methods in the theory of differential equations on manifolds with singularities are presented. The semiclassical theory in quantum mechanics is employed, adapted to operators that are degenerate in a typical way. The degeneracies may be induced by singular geometries, e.g., conical or cuspidal ones. A large variety of non-standard degenerate operators are also discussed. The semiclassical approach yields new results and unexpected effects, also in classical situations. For instance, full asymptotic expansions for cuspidal singularities are constructed, and nonstationary problems on singular manifolds are treated. Moreover, finiteness theorems are obtained by using operator algebra methods in a unified framework. Finally the method of characteristics for general elliptic equations on manifolds with singularities is developed in the book.

Table of Contents:
GENERALITIES; Structure Rings on Singular Manifolds; Interaction of Asymptotic Expansions; Resurgent Analysis of Functions of Polynomial Growth; ELLIPTIC EQUATIONS; Asymptotic Solutions on Manifolds with Conical Singularities; Asymptotic Solutions on Manifolds with Cusp-Type Singularities; Asymptotic Solutions on Manifolds with Corner-Type Singularities; General Asymptotic Theory; Finiteness Theorems; HYPERBOLIC EQUATIONS; Equations of Borel-Fuchs Type; Vibration of Elastic Shells with Conical Points; Appendices; Bibliography; Index.

Review :
."..much useful information..." (Bulletin of the Belgium Mathematical Society) ..".much useful information..." (Bulletin of the Belgium Mathematical Society)


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Product Details
  • ISBN-13: 9783527400867
  • Publisher: Wiley-VCH Verlag GmbH
  • Publisher Imprint: Wiley-VCH Verlag GmbH
  • Height: 244 mm
  • Returnable: N
  • Sub Title: Semiclassical Theory and Operator Algebras
  • Width: 174 mm
  • ISBN-10: 3527400869
  • Publisher Date: 17 Dec 1998
  • Binding: Hardback
  • Language: English
  • Series Title: Mathematical Topics S.
  • Weight: 920 gr


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Differential Equations on Singular Manifolds: Semiclassical Theory and Operator Algebras(Mathematical Topics S.)
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Differential Equations on Singular Manifolds: Semiclassical Theory and Operator Algebras(Mathematical Topics S.)
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