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 St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(e) ISSN 1061-0022(p)

     
     

Mikhail Shlemovich Birman (on the occasion of his 75th birthday)

Author(s): V. S. Buslaev; M. Z. Solomyak; D. R. Yafaev
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 16 (2004), vypusk 1.
Journal: St. Petersburg Math. J. 16 (2005), 1-8.
MSC (2000): Primary 01A70
Posted: December 14, 2004
MathSciNet review: 2068350
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\begin{extrabibtext}\slshape Earlier surveys and publications (items $[135^*]-[141^*]$\space have the same numbers as in $[2^*]$ ). \end{extrabibtext}

[$1^*$]
V. Buslaev, M. Solomyak, and D. Yafaev, On the scientific work of Mikhail Shlemovich Birman, Differential Operators and Spectral Theory (V. Buslaev, M. Solomyak, D. Yafaev, eds.), Amer. Math. Soc. Transl. Ser. 2, vol. 189, Amer. Math. Soc., Providence, RI, 1999, pp. 1-15. MR 1730499 (2000k:01029a)

[$2^*$]
V. Buslaev, M. Solomyak, and D. Yafaev (eds.), List of publications of M. Sh. Birman, Differential Operators and Spectral Theory, Amer. Math. Soc. Transl. Ser. 2, vol. 189, Amer. Math. Soc., Providence, RI, 1999, pp. 17-26. MR 1730498 (2000g:00083)

[$3^*$]
V. S. Buslaev, A. M. Vershik, I. M. Gel'fand, et al., Mikhail Shlëmovich Birman (on the occasion of his seventieth birthday), Uspekhi Mat. Nauk 55 (2000), no. 1, 204-207; English transl., Russian Math. Surveys 55 (2000), no. 1, 201-205. MR 1751834 (2000m:01033)

[$135^*$]
M. Sh. Birman and A. B. Pushnitskii, The discrete spectrum in the gaps of the perturbed pseudo-relativistic magnetic Hamiltonian, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 249 (1997), 102-117; English transl., J. Math. Sci. 101 (2000), no. 5, 3437-3447. MR 1698515 (2000h:35123)

[$138^*$]
M. Sh. Birman and T. A. Suslina, Absolute continuity of the two-dimensional periodic magnetic Hamiltonian with discontinuous vector-valued potential, Algebra i Analiz 10 (1998), no. 4, 1-36; English transl., St. Petersburg Math. J. 10 (1999), no. 4, 579-601. MR 1654063 (99k:81060)

[$139^*$]
-, Two-dimensional periodic Pauli operator. The effective masses at the lower edge of the spectrum, Mathematical Results in Quantum Mechanics (Prague, 1998), Oper. Theory Adv. Appl., vol. 108, Birkhäuser, Basel, 1999, pp. 13-31. MR 1708785 (2000g:81049)

[$140^*$]
-, The periodic Dirac operator is absolutely continuous, Integral Equations Operator Theory 34 (1999), no. 4, 377-395. MR 1702229 (2000h:47068)

[$141^*$]
-, Periodic magnetic Hamiltonian with variable metric. The problem of absolute continuity, Algebra i Analiz 11 (1999), no. 2, 1-40; English transl., St. Petersburg Math. J. 11 (2000), no. 2, 203-232. MR 1702587 (2000i:35026)


\begin{extrabibtext}\slshape Continuation of the list of publications by M. S. Birman (see $[2^*]$ ) \end{extrabibtext}

[1]
M. Sh. Birman and T. A. Suslina, On the absolute continuity of the periodic Schrödinger and Dirac operators with magnetic potential, Differential Equations and Mathematical Physics (Birmingham, AL, 1999), AMS/IP Stud. Adv. Math., vol. 16, Amer. Math. Soc., Providence, RI, 2000, pp. 41-49. MR 1764740

[2]
-, Threshold effects near the lower edge of the spectrum for periodic differential operators of mathematical physics, Systems, Approximation, Singular Integral Operators, and Related Topics (Bordeaux, 2000), Oper. Theory Adv. Appl., vol. 129, Birkhäuser, Basel, 2001, pp. 71-107. MR 1882692 (2003f:35220)

[3]
M. Sh. Birman, A. A. Laptev, and T. A. Suslina, Discrete spectrum of a two-dimensional periodic elliptic second order operator perturbed by a decaying potential. . Semibounded gap, Algebra i Analiz 12 (2000), no. 4, 36-78; English transl., St. Petersburg Math. J. 12 (2001), no. 4, 535-567. MR 1793617 (2003b:47078)

[4]
M. Sh. Birman, R. G. Shterenberg, and T. A. Suslina, Absolute continuity of the spectrum of a two-dimensional Schrödinger operator with potential supported on a periodic system of curves, Algebra i Analiz 12 (2000), no. 6, 140-177; English transl., St. Petersburg Math. J. 12 (2001), no. 6, 983-1012. MR 1816514 (2002k:35227)

[5]
M. Sh. Birman and M. Solomyak, On the negative discrete spectrum of a periodic elliptic operator in a waveguide-type domain, perturbed by a decaying potential, J. Anal. Math. 83 (2001), 337-391. MR 1828497 (2002k:35226)

[6]
B. A. Amosov, M. Sh. Birman, M. I. Vishik, et al., Mikhail Semenovich Agranovich (on the occasion of his seventieth birthday), Uspekhi Mat. Nauk 56 (2001), no. 4, 163-168; English transl., Russian Math. Surveys 56 (2001), no. 4, 777-784. MR 1861459 (2002h:01026)

[7]
M. Sh. Birman and T. A. Suslina, Absolute continuity of the spectrum of the periodic operator of elasticity theory for constant shear modulus, Nonlinear Problems in Mathematical Physics and Related Topics, II (in honor of prof. O. A. Ladyzhenskaya) (M. Birman, S. Hildebrandt, V. Solonnikov, N. Ural'tseva, eds.), Int. Math. Ser. (N.Y.), vol. 2, Kluwer/Plenum, New York, 2002, pp. 69-74. MR 1971990 (2004c:35296)

[8]
A. A. Arkhipova, M. Sh. Birman, V. S. Buslaev, et al., On the jubilee of Ol'ga Aleksandrovna Ladyzhenskaya, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 288 (2002), 5-13. (Russian) MR 1923542

[9]
M. Birman, S. Hildebrandt, V. Solonnikov, and N. Ural'tseva (eds.), Nonlinear problems in mathematical physics and related topics, I (in honor of prof. O. A. Ladyzhenskaya), Int. Math. Ser. (N.Y.), vol. 1, Kluwer/Plenum, New York, 2002, 386 pp. MR 1971549 (2003m:35003)

[10]
-, Nonlinear problems in mathematical physics and related topics, II (in honor of prof. O. A. Ladyzhenskaya), Int. Math. Ser. (N.Y.), vol. 2, Kluwer/Plenum, New York, 2002, 380 pp. MR 1971985 (2003m:35004)

[11]
M. Sh. Birman, On homogenization procedure for periodic operators near the edge of an internal gap, Algebra i Analiz 15 (2003), no. 4, 61-71; English transl., St. Petersburg Math. J. 15 (2004), no. 4, 507-513. MR 2068979

[12]
M. Sh. Birman and T. A. Suslina, Second order periodic differential operators. Threshold properties and homogenization, Algebra i Analiz 15 (2003), no. 5, 1-108; English transl., St. Petersburg Math. J. 15 (2004), no. 5, 639-714. MR 2068790

[13]
M. Birman and M. Solomyak, Double operator integrals in a Hilbert space, Integral Equations Operator Theory 47 (2003), no. 2, 131-168. MR 2002663 (2004f:47029)

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DOI: 10.1090/S1061-0022-04-00841-6
PII: S 1061-0022(04)00841-6
Received by editor(s): 10/NOV/2003
Posted: December 14, 2004
Copyright of article: Copyright 2004, American Mathematical Society




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