Birman, M. Sh.; Sloushch, V. A. Discrete spectrum of the periodic Schrödinger operator with a variable metric perturbed by a nonnegative potential. (English) Zbl 1207.47041 Math. Model. Nat. Phenom. 5, No. 4, 32-53 (2010). Reviewer: Vladimir S. Pilidi (Rostov-na-Donu) MSC: 47F05 47G10 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{V. A. Sloushch}, Math. Model. Nat. Phenom. 5, No. 4, 32--53 (2010; Zbl 1207.47041) Full Text: DOI EuDML
Alekseev, A. B.; Birman, M. Sh.; Filonov, N. D. Spectrum asymptotics for one “nonsmooth” variational problem with solvable constraint. (English. Russian original) Zbl 1260.35092 St. Petersbg. Math. J. 18, No. 5, 681-697 (2007); translation from Algebra Anal. 18, No. 5, 1-22 (2006). MSC: 35P20 35S05 47F05 47G30 49J52 PDFBibTeX XMLCite \textit{A. B. Alekseev} et al., St. Petersbg. Math. J. 18, No. 5, 681--697 (2007; Zbl 1260.35092); translation from Algebra Anal. 18, No. 5, 1--22 (2006) Full Text: DOI
Birman, M. Sh.; Filonov, N. D. Weyl asymptotic of the spectrum of the Maxwell operator with non-smooth coefficients in Lipschitz domains. (English) Zbl 1260.35096 Birman, M. S. (ed.) et al., Nonlinear equations and spectral theory. Dedicated to the memory of Olga Aleksandrovna Ladyzhenskaya. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4209-6/hbk). Translations. Series 2. American Mathematical Society 220. Advances in the Mathematical Sciences 59, 27-44 (2007). MSC: 35P25 35Q61 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{N. D. Filonov}, Transl., Ser. 2, Am. Math. Soc. 220, 27--44 (2007; Zbl 1260.35096)
Birman, M. Sh.; Pushnitskii, A. B. Discrete spectrum in the gaps of a perturbed pseudorelativistic Hamiltonian. (English. Russian original) Zbl 0966.83005 J. Math. Sci., New York 101, No. 5, 3437-3447 (2000); translation from Zap. Nauchn. Semin. POMI 249, 102-117 (1997). MSC: 83A05 35Q75 81T20 47A10 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{A. B. Pushnitskii}, J. Math. Sci., New York 101, No. 5, 1 (1997; Zbl 0966.83005); translation from Zap. Nauchn. Semin. POMI 249, 102--117 (1997) Full Text: DOI
Birman, Mikhail Sh.; Laptev, Ari “Non-standard” spectral asymptotics for a two-dimensional Schrödinger operator. (English) Zbl 0910.35086 Greiner, Peter C. (ed.) et al., Partial differential equations and their applications. Lectures given at the 1995 annual seminar of the Canadian Mathematical Society, Toronto, Canada, June 12–23, 1995. Providence, RI: American Mathematical Society. CRM Proc. Lect. Notes. 12, 9-16 (1997). Reviewer: J.Rákosník (Praha) MSC: 35P20 35J10 35P15 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{A. Laptev}, in: Partial differential equations and their applications. Lectures given at the 1995 annual seminar of the Canadian Mathematical Society, Toronto, Canada, June 12--23, 1995. Providence, RI: American Mathematical Society. 9--16 (1997; Zbl 0910.35086)
Birman, M. Sh. The discrete spectrum in gaps of the perturbed periodic Schrödinger operator. I: Regular perturbations. (English) Zbl 0848.47032 Demuth, Michael (ed.) et al., Boundary value problems, Schrödinger operators, deformation quantization. Berlin: Akademie Verlag. Math. Top. 8, 334-352 (1995). Reviewer: M.Perelmuter (Kiev) MSC: 47F05 35P20 47A55 PDFBibTeX XMLCite \textit{M. Sh. Birman}, Math. Top. 8, 334--352 (1995; Zbl 0848.47032)
Birman, M. Sh.; Weidl, T. The discrete spectrum in a gap of the continuous one for compact supported perturbations. (English) Zbl 0824.35090 Demuth, Michael (ed.) et al., Mathematical results in quantum mechanics: International conference in Blossin (Germany), May 17-21, 1993. Basel: Birkhäuser Verlag. Oper. Theory, Adv. Appl. 70, 9-12 (1994). Reviewer: M.Perelmuter (Kiev) MSC: 35P20 47A55 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{T. Weidl}, in: Mathematical results in quantum mechanics: International conference in Blossin (Germany), May 17-21, 1993. Basel: Birkhäuser Verlag. 9--12 (1994; Zbl 0824.35090)
Birman, M. Sh.; Yafaev, D. R. Scattering matrix for the perturbation of a periodic Schrödinger operator by a decaying potential. (English. Russian original) Zbl 0860.35088 St. Petersbg. Math. J. 6, No. 3, 453-474 (1995); translation from Algebra Anal. 6, No. 3, 17-39 (1994). Reviewer: B.Pavlov (Auckland) MSC: 35P25 47A40 35J10 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{D. R. Yafaev}, St. Petersbg. Math. J. 6, No. 3, 17--39 (1994; Zbl 0860.35088); translation from Algebra Anal. 6, No. 3, 17--39 (1994)
Birman, Mikhail Sh.; Laptev, Ari Discrete spectrum of the perturbed Dirac operator. (English) Zbl 0822.35104 Ark. Mat. 32, No. 1, 13-32 (1994). MSC: 35P20 35Q40 35S05 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{A. Laptev}, Ark. Mat. 32, No. 1, 13--32 (1994; Zbl 0822.35104) Full Text: DOI
Birman, M. Sh. Discrete spectrum of the periodic elliptic operator with a differential perturbation. (English) Zbl 0875.35062 Journ. Équ. Dériv. Partielles, St.-Jean-de-Monts 1994, Exp. No. 14, 4 p. (1994). MSC: 35P05 35B25 35J10 PDFBibTeX XMLCite \textit{M. Sh. Birman}, Journ. Équ. Dériv. Partielles, St.-Jean-de-Monts 1994, Exp. No.~14, 4~p. (1994; Zbl 0875.35062) Full Text: Numdam EuDML
Birman, M. Sh. Discrete spectrum in the gaps of a continuous one for perturbations with large coupling constant. (English) Zbl 0754.35025 Estimates and asymptotics for discrete spectra of integral and differential equations, Pap. Semin. Math. Phys., Leningrad/Russia 1989-90, Adv. Sov. Math. 7, 57-73 (1991). Reviewer: G.Nenciu (Bucureşti) MSC: 35J10 47A75 35P20 PDFBibTeX XMLCite \textit{M. Sh. Birman}, Adv. Sov. Math. 7, 57--73 (1991; Zbl 0754.35025)
Birman, M. Sh. (ed.) Estimates and asymptotics for discrete spectra of integral and differential equations. Papers of the Leningrad seminar on mathematical physics in the academic year of 1989-90. Transl. ed. by A. B. Sossinsky. (English) Zbl 0741.00022 Advances in Soviet Mathematics. 7. Providence, RI: American Mathematical Society (AMS). x, 204 p. (1991). MSC: 00B15 35-06 47-06 PDFBibTeX XMLCite \textit{M. Sh. Birman} (ed.), Estimates and asymptotics for discrete spectra of integral and differential equations. Papers of the Leningrad seminar on mathematical physics in the academic year of 1989-90. Transl. ed. by A. B. Sossinsky. Providence, RI: American Mathematical Society (1991; Zbl 0741.00022)
Birman, M. Sh.; Solomyak, M. Z. The Weyl asymptotics of the spectrum of the Maxwell operator for domains with a Lipschitz boundary. (English. Russian original) Zbl 0639.35062 Vestn. Leningr. Univ., Math. 20, No. 3, 15-21 (1987); translation from Vestn. Leningr. Univ., Ser. I 1987, No. 3, 23-28 (1987). MSC: 35P20 35Q61 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{M. Z. Solomyak}, Vestn. Leningr. Univ., Math. 20, No. 3, 15--21 (1987; Zbl 0639.35062); translation from Vestn. Leningr. Univ., Ser. I 1987, No. 3, 23--28 (1987)
Birman, M. Sh. Quasiclassical spectral asymptotics of one class of integral operators. (English) Zbl 0502.47027 J. Sov. Math. 21, 12-20 (1983). MSC: 47Gxx 62G05 35S05 PDFBibTeX XMLCite \textit{M. Sh. Birman}, J. Sov. Math. 21, 12--20 (1983; Zbl 0502.47027) Full Text: DOI
Birman, M. Sh.; Solomyak, M. Z. Asymptotics of the spectrum of variational problems on solutions of elliptic equations in unbounded domains. (English. Russian original) Zbl 0463.35061 Funct. Anal. Appl. 14, 267-274 (1981); translation from Funkts. Anal. Prilozh. 14, No. 4, 27-35 (1980). MSC: 35P20 35R20 47F05 35J20 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{M. Z. Solomyak}, Funct. Anal. Appl. 14, 267--274 (1981; Zbl 0463.35061); translation from Funkts. Anal. Prilozh. 14, No. 4, 27--35 (1980) Full Text: DOI
Birman, M. Sh.; Solomyak, M. Z. On the asymptotics of the spectrum of variational problems on solutions of elliptic equations. (Russian) Zbl 0495.35064 Partial differential equations: differential equations and numerical mathematics, Work Collect. Conf., Novosibirsk 1978, 221-223 (1980). MSC: 35P20 35J30 PDFBibTeX XML
Birman, M. Sh.; Solomyak, M. Z. The asymptotics of the spectrum of pseudodifferential operators with anisotropic-homogeneous symbols. II. (English) Zbl 0461.47025 Vestn. Leningr. Univ., Math. 12, 155-161 (1980). MSC: 47Gxx 47A10 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{M. Z. Solomyak}, Vestn. Leningr. Univ., Math. 12, 155--161 (1980; Zbl 0461.47025)
Birman, M. Sh. On the quasi-classical spectral asymptotics of a class of integral operators. (Russian) Zbl 0451.47066 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 98, 22-32 (1980). MSC: 47Gxx 62G05 PDFBibTeX XMLCite \textit{M. Sh. Birman}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 98, 22--32 (1980; Zbl 0451.47066) Full Text: EuDML
Birman, M. Sh.; Solomyak, M. Z. Asymptotics of the spectrum of variational problems on solutions of elliptic equations. (English) Zbl 0427.35050 Sib. Math. J. 20, 1-15 (1979). MSC: 35P20 47F05 35J35 49R50 35S15 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{M. Z. Solomyak}, Sib. Math. J. 20, 1--15 (1979; Zbl 0427.35050) Full Text: DOI EuDML
Birman, M. Sh.; Solomyak, M. Z. Asymptotic behavior of the spectrum of differential equations. (English) Zbl 0424.35069 J. Sov. Math. 12, 247-283 (1979). MSC: 35P20 47F05 PDFBibTeX XMLCite \textit{M. Sh. Birman} and \textit{M. Z. Solomyak}, J. Sov. Math. 12, 247--283 (1979; Zbl 0424.35069) Full Text: DOI