
Spectral asymptotics for infinite order pseudo-differential operators
- Author
- Stevan Pilipović, Bojan Prangoski and Jasson Vindas Diaz (UGent)
- Organization
- 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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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8584742
- 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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