Literature Cited
R. S. Saks, “Weakly elliptic boundary-value problems,” in: Partial Differential Equations [in Russian], No. 2, Trudy Sem. S. L. Soboleva, Institute of Mathematics, Siberian Branch of the Academy of Sciences of the USSR (1980), pp. 57–78.
V. I. Bezyaev, “The asymptotics of the eigenvalues of hypoelliptic operators on a closed manifold,” Dokl. Akad. Nauk SSSR,244, No. 5, 1054–1057 (1979).
V. I. Bezyaev, “The asymptotic behavior of the eigenvalues of hypoelliptic operators on a closed manifold,” Mat. Sb.,117, (159), No. 2, 161–180 (1982).
M. Sh. Birman and M. Z. Solomyak, “The asymptotic behavior of the spectra of differential equations,” J. Sov. Math.,12, No. 3 (1979).
V. Ya. Ivrii, “The asymptotic behavior of the eigenvalues for certain elliptic operators acting in vector bundles over a manifold with boundary,” Dokl. Akad. Nauk SSSR,258, No. 1, 1045–1047 (1981).
V. Ya. Ivrii, “The asymptotic behavior of eigenvalues for a certain class of elliptic operators, acting in fiber bundles over a manifold with boundary,” Dokl. Akad. Nauk SSSR,263, No. 3, 530–532 (1982).
G. Grubb, “Estimation du reste dans l'ètude des valeurs propres des problemes aux limites pseudodifferentiels auto-adjoints,” C. R. Acad. Sci. Paris,287, Ser. A-B, A1017-A1020 (1978).
G. Grubb, “Remainder estimates for eigenvalues and kernels of psuedodifferential elliptic systems,” Math. Scand.,43, 275–307 (1978).
G. Grubb, “Spectral asymptotics for Douglis-Nirenberg elliptic and pseudodifferential boundary problems,” Commun. Partial Diff. Eqs.,2, No. 11, 1071–1150 (1977).
A. N. Kozhevnikov, “Spectral problems for pseudodifferential systems, elliptic in the Douglis-Nirenberg sense, and their applications,” Mat. Sb.,92, (134), No. 1, 60–88 (1973).
A. N. Kozhevnikov, “Remainder estimate for spectral asymptotics and complex powers of Douglis-Nirenberg elliptic systems,” Dokl. Akad. Nauk SSSR,254, No. 1, 32–35 (1980).
V. N. Tulovskii and M. A. Shubin, “On the asymptotic distribution of the eigenvalues of pseudodifferential operators in Rn,” Mat. Sb.,92, (134), No. 4, 571–588 (1973).
V. I. Feigin, “The asymptotic distribution of eigenvalues for hypoelliptic systems in Rn,” Mat. Sb.,99, (141), No. 4, 594–614 (1976).
V. I. Feigin, “The asymptotic distribution of eigenvalues and a formula of Bohr-Sommerfeld type,” Mat. Sb.,110, (152), No. 1, 66–87 (1979).
V. I. Feigin, “On the spectral asymptotics for boundary value problems, and the asymptotic behavior of the negative spectrum,” Dokl. Akad. Nauk SSSR,232, No. 6, 1269–1272 (1977).
S. Z. Levendorskii, “Algebras of pseudodifferential operators with discontinuous symbols,” Dokl. Akad. Nauk SSSR,248, No. 4, 777–779 (1979).
S. Z. Levendorskii, “On a general method for investigating the asymptotic behavior of the spectrum and its application to the theory of shells,” Dokl. Akad. Nauk SSSR,266, No. 2, 276–280 (1982).
S. Z. Levendorskii, “The asymptotic distribution of eigenvalues,” Izv. Akad. Nauk SSSR, Ser. Mat.,46, No. 4, 810–852 (1982).
L. Hörmander, “On the asymptotic distribution of the eigenvalues of pseudodifferential operators in Rn,” Ark. Mat.,17, No. 2, 297–313 (1979).
L. Hörmander, “The Weyl calculus of pseudodifferential operators,” Commun. Pure Appl. Math.,32, 359–443 (1979).
L. Hörmander, “Fourier integral operators. I,” Acta Math.,127, Nos. 1–2, 79–183 (1971).
M. A. Shubin, Pseudodifferential Operators and Spectral Theory [in Russian], Nauka, Moscow (1978).
R. Beals, “A general calculus of pseudodifferential operators,” Duke Math. J.,42, No. 1, 1–42 (1975).
Additional information
Rostov-on-the-Don. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 27, No. 1, pp. 111–122, January–February, 1985.
Rights and permissions
About this article
Cite this article
Levendorskii, S.Z. Asymptotic behavior of the spectra of weakly elliptic systems of pseudodifferential operators. Sib Math J 27, 89–99 (1986). https://doi.org/10.1007/BF00969346
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00969346