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The Spectral Counting Function N(λ) and the Behavior of the Eigenvalues: Part 1

Part of the Lecture Notes in Mathematics book series (LNM,volume 1992)

Abstract

To understand the eigenvalues of an elliptic global operator, a very useful, basic and general tool is the Minimax Principle. After recalling it, we shall use the Minimax Principle to study the first properties of the spectral counting function, and of the behavior of the large eigenvalues, of an elliptic global operator. Remark that everything we say in this section holds also for matrix-valued operators.

Keywords

  • Harmonic Oscillator
  • Large Eigenvalue
  • Discrete Spectrum
  • Principal Symbol
  • Compact Resolvent

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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Correspondence to Alberto Parmeggiani .

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Parmeggiani, A. (2010). The Spectral Counting Function N(λ) and the Behavior of the Eigenvalues: Part 1. In: Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction. Lecture Notes in Mathematics(), vol 1992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11922-4_4

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