Abstract
A new class of degenerate pseudodifferential operators with a variable symbol depending on a complex parameter is investigated. Pseudodifferential operators are constructed by applying a special integral transform. Theorems on the composition and boundedness of these operators in special weighted spaces are proved. The behavior of these operators on hyperplanes of degeneration is investigated. Theorems on the commutation of these operators with differentiation operators are established. An adjoint operator is constructed, and an analogue of Gårding’s inequality for degenerate pseudodifferential operators is proved.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
M. V. Keldysh, Dokl. Akad. Nauk SSSR 77 (2), 181–183 (1951).
M. I. Vishik and V. V. Grushin, Math. USSR-Sb. 8 (1), 1–32 (1969).
A. D. Baev, Dokl. Akad. Nauk SSSR 265 (5), 1044–1046 (1982).
A. D. Baev, Dokl. Math. 78 (2), 763–764 (2008).
S. Z. Levendorskii, Math. USSR-Sb. 39 (4), 429–447 (1981).
A. D. Baev and P. A. Kobylinskii, Dokl. Math. 91 (1), 23–25 (2015).
A. D. Baev and R. A. Kovalevskii, Dokl. Math. 89 (1), 1–4 (2014).
Funding
This work was supported by the Ministry of Education and Science of the Russian Federation, project no. 14.Z50.31.0037.
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by I. Ruzanova
Rights and permissions
About this article
Cite this article
Baev, A.D., Babaytsev, A.A. & Kharchenko, V.D. On Some Degenerate Pseudodifferential Operators. Dokl. Math. 100, 459–462 (2019). https://doi.org/10.1134/S106456241905017X
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S106456241905017X