Abstract
We study the self-adjointness and spectral structure of general first-order partial differential operators (including the nonstationary two-dimensional Dirac operator) and the structure of the resolvent of the two-dimensional Dirac operator.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Yu. M. Berezanskii,Expansion in Eigenfunctions of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).
L. P. Nizhnik, “On the spectrum of general differential operators,”Dokl. Akad. Nauk SSSR,124, No. 3, 517–519 (1959).
L. P. Nizhnik, “Spectral structure and self-adjointness of perturbations of differential operators with constant coefficients,”Ukr. Mat. Zh.,15, No. 4, 385–399 (1963).
L. P. Nizhnik, “Spectral properties of self-adjoint partial differential operators which are close to the operators with constant coefficients,” in:Proceedings of the Joint Soviet-American Symposium on Partial Differential Equations (Novosibirsk, 1963), Izd. Akad. Nauk SSSR, Moscow (1963), pp. 195–199.
M. Schechter,Spectra of Partial Differential Operators, North-Holland, Amsterdam (1971).
V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii,Theory of Solitons. Method of Inverse Problems [in Russian], Nauka, Moscow (1980).
L. P. Nizhnik and M. D. Pochinaiko, “Integration of the spatially-two-dimensional nonlinear Schrödinger equation by the method of inverse problems,”Funkts. Anal.,16, No. 1, 80–82 (1982).
L. P. Nizhnik,Inverse Scattering Problems for Hyperbolic Equations [in Russian], Naukova Dumka, Kiev (1991).
E. I. Amerova and L. P. Nizhnik, “Spectral analysis of the two-dimensional Dirac operator,” in:Boundary-Value Problems for Differential Equations [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1988), pp. 4–5.
L. P. Nizhnik and V. G. Tarasov, “Many-dimensional inverse scattering problem for a system of first-order partial differential equations,” in:Boundary-Value Problems for Differential Equations, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1992), pp. 84–93.
T. Kato,Perturbation Theory for Linear Operators, Springer-Verlag, Berlin (1966).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 5, pp. 593–599, May, 1995.
This work was partially supported by the Foundation for Fundamental Research of the Ukrainian State Committee on Science and Technology.
Rights and permissions
About this article
Cite this article
Amerova, E.I., Nizhnik, L.P. Spectral properties of the nonstationary two-dimensional Dirac operator. Ukr Math J 47, 686–693 (1995). https://doi.org/10.1007/BF01059041
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01059041