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Spectral asymptotics for infinite order pseudo-differential operators

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Abstract
We study spectral properties of a class of global infinite order pseudo-differential operators and obtain the asymptotic behaviour of the spectral counting functions of such operators. Unlike their finite order counterparts, their spectral asymptotics are not of power-log-type but of log-type. The ultradistributional setting of such operators of infinite order makes the theory more complex so that the standard finite order global Weyl calculus cannot be used in this context.
Keywords
Weyl asymptotic formula, Spectral asymptotics, Infinite order pseudo-differential operators, Hypoellipticity, Heat parametrix, Ultradistributions, TEMPERED ULTRADISTRIBUTIONS, SPACES

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MLA
Pilipović, Stevan, et al. “Spectral Asymptotics for Infinite Order Pseudo-Differential Operators.” BULLETIN OF MATHEMATICAL SCIENCES, vol. 8, no. 1, 2018, pp. 81–120, doi:10.1007/s13373-017-0114-9.
APA
Pilipović, S., Prangoski, B., & Vindas Diaz, J. (2018). Spectral asymptotics for infinite order pseudo-differential operators. BULLETIN OF MATHEMATICAL SCIENCES, 8(1), 81–120. https://doi.org/10.1007/s13373-017-0114-9
Chicago author-date
Pilipović, Stevan, Bojan Prangoski, and Jasson Vindas Diaz. 2018. “Spectral Asymptotics for Infinite Order Pseudo-Differential Operators.” BULLETIN OF MATHEMATICAL SCIENCES 8 (1): 81–120. https://doi.org/10.1007/s13373-017-0114-9.
Chicago author-date (all authors)
Pilipović, Stevan, Bojan Prangoski, and Jasson Vindas Diaz. 2018. “Spectral Asymptotics for Infinite Order Pseudo-Differential Operators.” BULLETIN OF MATHEMATICAL SCIENCES 8 (1): 81–120. doi:10.1007/s13373-017-0114-9.
Vancouver
1.
Pilipović S, Prangoski B, Vindas Diaz J. Spectral asymptotics for infinite order pseudo-differential operators. BULLETIN OF MATHEMATICAL SCIENCES. 2018;8(1):81–120.
IEEE
[1]
S. Pilipović, B. Prangoski, and J. Vindas Diaz, “Spectral asymptotics for infinite order pseudo-differential operators,” BULLETIN OF MATHEMATICAL SCIENCES, vol. 8, no. 1, pp. 81–120, 2018.
@article{8584742,
  abstract     = {{We study spectral properties of a class of global infinite order pseudo-differential operators and obtain the asymptotic behaviour of the spectral counting functions of such operators. Unlike their finite order counterparts, their spectral asymptotics are not of power-log-type but of log-type. The ultradistributional setting of such operators of infinite order makes the theory more complex so that the standard finite order global Weyl calculus cannot be used in this context.}},
  author       = {{Pilipović, Stevan and Prangoski, Bojan and Vindas Diaz, Jasson}},
  issn         = {{1664-3607}},
  journal      = {{BULLETIN OF MATHEMATICAL SCIENCES}},
  keywords     = {{Weyl asymptotic formula,Spectral asymptotics,Infinite order pseudo-differential operators,Hypoellipticity,Heat parametrix,Ultradistributions,TEMPERED ULTRADISTRIBUTIONS,SPACES}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{81--120}},
  title        = {{Spectral asymptotics for infinite order pseudo-differential operators}},
  url          = {{http://doi.org/10.1007/s13373-017-0114-9}},
  volume       = {{8}},
  year         = {{2018}},
}

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