Abstract
In this paper, we find the asymptotics of integrated density of states with remainder estimate for hypoelliptic systems with almost periodic (a.p.) coefficients. We use the approximate spectral projector method for matrix a.p. operators with continuous spectrum.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. I. Bezyaev, “Asymptotics of the density of states of hypoelliptic almost periodic operators,” Mat. Sb., 24, No. 7, 485–511 (1978).
L. A. Coburn, R. D. Moyer, and I. M. Singer, “C*-algebras of almost periodic pseudo-differential operators,” Acta Math., 130, 279–307 (1973).
J. Dixmier, Les Algebres d’Operateurs dans l’Espace Hilbertien (Algebres de von Neumann), Gauthier-Villars, Paris (1969).
V. I. Feygin, “Asymptotic distribution of eigenvalues for hypoelliptic systems in ℝn,” Mat. Sb., 99, No. 4, 594–614 (1976).
L. Hörmander, The Analysis of Linear Partial Differential Operators. I [Russian translation], Mir, Moscow (1986).
L. Hörmander, The Analysis of Linear Partial Differential Operators. III [Russian translation], Mir, Moscow (1987).
A. I. Karol’, “Asymptotic behavior of the spectrum of pseudodifferential operators of variable order,” J. Math. Sci. (N.Y.), 207, No. 2, 236–248 (2015).
H. Kumano-go, “Algebras of pseudo-differential operators,” J. Fac. Sci. Univ. Tokyo. Sec. 1A, 17, 31–50 (1970).
S. Z. Levendorskiy, “Method of approximate spectral projector,” Izv. AN SSSR. Ser. Mat., 49, No. 6, 1177–1228 (1985).
G. V. Rozenblyum, M. Z. Solomyak, and M. A. Shubin, “Spectral theory of differential operators,” Itogi Nauki i Tekhn. Sovrem. Probl. Mat., 64, 5–242 (1989).
M. A. Shubin, “Pseudodifferential almost periodic operators and von Neumann algebras,” Tr. Mosk. Mat. Ob-va, 35, 103–164 (1976).
M. A. Shubin, “The Weil theorem for the Schr¨odinger operator with almost periodic potential,” Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., No. 2, 84–88 (1976).
M. A. Shubin, “Density of states for self-adjoint elliptic operators with almost periodic coefficients,” Tr. Sem. im. I. G. Petrovskogo, 3, 243–275 (1978).
V. N. Tulovskiy and M. A. Shubin, “On asymptotic distribution of eigenvalues of pseudodifferential operators in Rn,” Mat. Sb., 92, No. 4, 571–588 (1973).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 65, No. 4, Proceedings of the S. M. Nikolskii Mathematical Institute of RUDN University, 2019.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Bezyaev, V.I. On Asymptotics of the Density of States for Hypoelliptic Almost Periodic Systems. J Math Sci 265, 763–773 (2022). https://doi.org/10.1007/s10958-022-06082-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-022-06082-6