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  3. The Technique of Pseudodifferential Operators
  • Cited by 86
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    • Publisher:
      Cambridge University Press
      Publication date:
      09 February 2010
      23 February 1995
      ISBN:
      9780511569425
      9780521378642
      DOI:
      https://doi.org/10.1017/CBO9780511569425
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.545kg, 396 Pages
      • Subjects:
      Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory
      Series:
      London Mathematical Society Lecture Note Series (202)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory
    Series:
    London Mathematical Society Lecture Note Series (202)
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    Book description

    Pseudodifferential operators arise naturally in the solution of boundary problems for partial differential equations. The formalism of these operators serves to make the Fourier-Laplace method applicable for nonconstant coefficient equations. This book presents the technique of pseudodifferential operators and its applications, especially to the Dirac theory of quantum mechanics. The treatment uses 'Leibniz formulas' with integral remainders or as asymptotic series. A pseudodifferential operator may also be described by invariance under action of a Lie-group. The author discusses connections to the theory of C*-algebras, invariant algebras of pseudodifferential operators under hyperbolic evolution and the relation of the hyperbolic theory to the propagation of maximal ideals. This book will be of particular interest to researchers in partial differential equations and mathematical physics.

    Reviews

    "...interesting and appropriate as a text for an introductory graduate course...it reflects the author's originality and experience in graduate teaching." Alexander Dynin, Bulletin of the American Mathematical Society

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