Abstract
In this chapter we shall describe the parametrix approximation of e-tA, A a positive elliptic global polynomial differential system, which will then be used, through Karamata’s Tauberian theorem (proved in Section 6.2), to compute the leading coefficient of the asymptotic behavior for large eigenvalues of the spectral counting function, in terms of the symbol of the system.
Keywords
- Pseudodifferential Operator
- Principal Symbol
- Fourier Integral Operator
- Smoothing Operator
- Spectral Zeta Function
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© 2010 Springer Berlin Heidelberg
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Parmeggiani, A. (2010). The Spectral Counting Function N(λ) and the Behavior of the Eigenvalues: Part 2. 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_6
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DOI: https://doi.org/10.1007/978-3-642-11922-4_6
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11921-7
Online ISBN: 978-3-642-11922-4
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