Literature Cited
N. N. Voitovich, B. Z. Katsenelenbaum, and A. N. Sivov, The Generalized Method of Characteristic Oscillations in Diffraction Theory [in Russian], Nauka, Moscow (1977).
A. Ya. Povzner and I. V. Sukharevskii, “Integral equations of second kind for problems of diffraction at an indefinitely thin screen,” Dokl. Akad. Nauk SSSR,127, No. 2, 291–294 (1959).
M. S. Agranovich, The Spectral Properties of Diffraction Problems [in Russian], “Appendix” in [1].
J. von Meixner, “Die Kantebedingung der Theorie der Beugung elektromagnetisher Wellen an vollkomen leitenden ebenen Schirme,” Ann. Phys.,6, No. 6, 1–9 (1949).
S. L. Sobolev, Introduction to the Theory of Cubature Formulas [in Russian], Nauka, Moscow (1974).
M. I. Vishik and V. V. Grushin, “On a class of degenerate elliptic equations of high orders,” Mat. Sb.,79, No. 1, 3–36 (1969).
V. V. Grushin, “On a class of elliptic pseudodifferential operators that degenerate on a submanifold,” Mat. Sb.,84, No. 2, 163–195 (1971).
R. Beals, “A general calculus of pseudodifferential operators,” Duke Math. J.,42, No. 1, 1–42 (1975).
R. Beals, “Characterization of pseudodifferential operators and applications,” Duke Math. J.,44, No. 1, 45–58 (1977).
V. V. Grushin, “Pseudodifferential operators in Rn with bounded symbols,” Funkts. Anal. Prilozhen.,4, No. 3, 37–50 (1970).
K. Taniguchi, “On the hypoellipticity and the global analytic hypoellipticity of pseudodifferential operators,” Osaka J. Math.,11, No. 2, 221–238 (1974).
V. I. Feigin, “Two algebras of pseudodifferential operators in Rn and certain applications,” Tr. Mosk. Mat. Obshch.,36, 155–194 (1977).
D. Robert, “Properties spectral d'operateurs pseudo-differentiales,” Commun. Part. Diff. Equat.,3, 755–826 (1978).
M. A. Shubin, Pseudodifferential Operators and Spectral Theory [in Russian], Nauka, Moscow (1978).
A. I. Komech, “Elliptic boundary-value problems for pseudodifferential operators on manifolds with conical points,” Mat. Sb.,86, No. 2, 268–298 (1971).
V. V. Grushin, “Hypoelliptic differential equations and pseudodifferential operators with operator-valued symbols,” Mat. Sb.,88, No. 4, 504–521 (1972).
V. P. Maslov, “Generalization of the notion of characteristic for A-pseudodifferential operators with operator-valued symbols,” Usp. Mat. Nauk,15, No. 6, 225–226 (1970).
K. Kh. Boimatov, “Pseudodifferential operators with an operator symbol,” Dokl. Akad. Nauk SSSR,244, No. 1, 20–23 (1979).
S. Z. Levendorskii, “Boundary-value problems in the half-space for quasielliptic pseudodifferential operators,” Mat. Sb.,111, No. 4, 483–502 (1980).
V. P. Glushko, “Estimates in L2 and solvability of general boundary-value problems for degenerate elliptic equations of second order,” Tr. Mosk. Mat. Obshch.,23, 113–178 (1970).
V. A. Kondrat'ev, “Singularities of the solution of the Dirichlet problem for an elliptic equation of second order in a neighborhood of the edge,” Differents. Uravn.,13, No. 11, 2026–2032 (1977).
V. G. Maz'ya and V. A. Plamenevskii, “On the coefficients in the asymptotic of the solutions of elliptic boundary-value problems near the edge,” Dokl. Akad. Nauk SSSR,229, No. 1, 33–36 (1976).
R. Narasimhan, Analysis on Real and Complex Manifolds, 1st edn., North-Holland, Amsterdam (1968).
J. L. Lions and E. Magenes, Non-Homogeneous Boundary-Value Problems and Applications, Springer-Verlag (1972).
S. G. Krein and Yu. I. Petunin, “Scales of Banach spaces,” Usp. Mat. Nauk,21, No. 2, 89–168 (1966).
L. Hörmander, “Pseudodifferential operators and nonelliptic boundary problems,” Ann. Math.,83, 129–209 (1966).
M. S. Agranovich and M. I. Vishik, “Elliptic problems with a parameter and parabolic problems of general form,” Usp. Mat. Nauk,19, No. 3, 53–161 (1964).
Additional information
Translated from Sibirskii Matematicheskii Zhurnal, Vol. 25, No. 1, pp. 39–52, January–February, 1984.
Rights and permissions
About this article
Cite this article
Berkhin, P.E. Problem of diffraction at a fine screen. Sib Math J 25, 31–42 (1984). https://doi.org/10.1007/BF00969506
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00969506