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The Eigenfunction Expansion Method

  • Ovidiu Calin
  • Der-Chen Chang
  • Kenro Furutani
  • Chisato Iwasaki
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

Finding the heat kernel of an elliptic operator on a compact manifold using the eigenvalues method is a well-known method in mathematical physics and quantum mechanics. Roughly speaking, the eigenvalues and eigenfunctions of an operator determine its heat kernel. The formula is an infinite series that involves products of eigenfunctions; see Theorem 6.1.1. It is interesting that in several cases this series can be written as an elementary function by using the associated bilinear generating function.

Keywords

Heat Kernel Gravitational Potential Hermite Polynomial Eigenfunction Expansion Complete Orthonormal System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Ovidiu Calin
    • 1
  • Der-Chen Chang
    • 2
  • Kenro Furutani
    • 3
  • Chisato Iwasaki
    • 4
  1. 1.Department of MathematicsEastern Michigan UniversityYpsilantiUSA
  2. 2.Department of Mathematics and StatisticsGeorgetown UniversityWashingtonUSA
  3. 3.Department of Mathematics ScienceUniversity of TokyoNodaJapan
  4. 4.Department of Mathematical ScienceUniversity of HyogoHimejiJapan

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