Acta Mathematica Hungarica

, Volume 71, Issue 4, pp 297–326 | Cite as

An extension of the Ikehara Tauberian theorem and its application

  • J. Aramaki
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    J. Aramaki, Complex powers of a class of pseudodifferential operators and their applications, Hokkaido Math. J., XII (1983), 199–225.Google Scholar
  2. [2]
    J. Aramaki, On the asymptotic behaviours of the spectrum of quasi-elliptic pseudo-differential operators on Rn, Tokyo J. Math., 10 (1987), 481–505.Google Scholar
  3. [3]
    J. Aramaki, On an extension of the Ikehara Tauberian theorem, Pacific J. Math., 133 (1988), 1–30.Google Scholar
  4. [4]
    J. Aramaki, Complex powers of vector valued operators and their applications to asymptotic behaviour of eigenvalues, J. Funct. Analysis, 87 (1989), 294–320.Google Scholar
  5. [5]
    W. Donoghue, Distributions and Fourier Transforms, Academic Press (New York, 1969).Google Scholar
  6. [6]
    J. J. Duistermaat and V. W. Guillemin, The spectrum of positive elliptic operators and periodic bicharacteristics, Invent. Math., 29 (1975), 39–79.Google Scholar
  7. [7]
    B. Helffer, Théorie spectrale pour des opérateurs globalement elliptiques, Société Math. de France, Astérisque (1984).Google Scholar
  8. [8]
    B. Helffer and D. Robert, Propriété asymptotiques du spectre d'opérateurs pseudodifférentiels sur R n, Comm. Partial Differential Equations, 7 (1982), 795–882.Google Scholar
  9. [9]
    B. Helffer and D. Robert, Calcul fonctionelle par la transformation de Mellin et opérateurs admissible, J. Functional Anal., 53 (1983), 246–268.Google Scholar
  10. [10]
    L. Hörmander, The Weyl calculus of pseudodifferential operators, Comm. Pure Appl. Math. 32 (1979), 359–443.Google Scholar
  11. [11]
    D. Robert, Comportement asymptotique des values propers d'opérateurs du type Schrödinger a potentiel dégénéré, J. Math. pures et appl., 61 (1982), 275–300.Google Scholar
  12. [12]
    R. T. Seeley, Complex powers of an elliptic operator, Singular integrals, Proc. Symp. Pure Math., Amer. Math. Soc., (1967), 288–307.Google Scholar
  13. [13]
    M. A. Shubin, Pseudodifferential Operators and Spectral Theory, Springer Verlag (Berlin, Heidelberg, New York, 1987).Google Scholar
  14. [14]
    N. Wiener, The Fourier Integral and Certain of its Applications, Dover Publ., Inc. (New York, 1958).Google Scholar

Copyright information

© Akadémiai Kiadó 1996

Authors and Affiliations

  • J. Aramaki
    • 1
  1. 1.Tokyo Denki UniversitySaitamaJapan

Personalised recommendations