Agranovich, Mikhail Semenovich

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Total publications: 54
Scientific articles: 44
Presentations: 2

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Doctor of physico-mathematical sciences (1967)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 4.01.1931
Keywords: strongly elliptic system, Lipschitz domain, Wiener-Hopf method, spectral asymptotics, completeness and basic property of root functions.
UDC: 514.76, 517.95, 517.958, 517.968, 517.98, 517.944.4, 517.9, 517.4, 517.43, 517.945.7, 517.984.5, 519.45
MSC: 31-XX, 35-XX, 46-XX, 47-XX, 58AXX, 58GXX, 35.55, 47A70, 47B25, 35S05, 35J99, 47G05, 58G15


About 70 scientific publications with results in the following fields: Methods of summation of divergent series, a theorem on the consistence (1953–54). Partial differential equations with constant coefficients, the existence of solutions and the construction of general solutions in some classes of usual functions and distributions, atest for smoothness of a d eneralized solution in a bounded domain (1958–61). General boundary value problems for elliptic systems, the equivalence of the ellipticity and of the Fredholm property of pseudodifferential boundary value problems; relative index theorems; the unique solvability of problems elliptic with parameter (1962–65). General mixed boundary value problems for parabolic systems in a cylindrical domain, the unique solvability (1963–67). Positive boundary value problems for symmetric and symmetrizable first order systems, the Fredholm property and the unique solvability (1966–69). General mixed boundary value problem for hyperbolic first order systems in a cylindrical domain with the uniform Lopatinskii condition, the development of the results due to Kreiss on the unique solvability (1971–72). Non-standard spectral problems for the Helmholtz equation and the Maxwell system, the basis property of the eigenfunctions and the completeness of the root functions, the localization and the asymptotic behavior of eigenvalues (1973–77). Non-self-adjoint operators that are weak perturbations of self-adjoint ones and operators far from being self-adjoint, the summability of Fourier series with respect to the root functions and the behavior of the eigenvalues (1976–92). Elliptic pseudo-differential operators on a closed curve, similarity transforms and asymptotic series for the eigenvalues and the eigenfunctions (1979–84). Relations between functions of an elliptic pseudodifferential operator, the asymptotics of the kernel of the resolvent with logarithmic terms, spectral asymptotics (1987–92). Spectral elliptic boundary value problems in Lipschitz domains, the investigation of the spectrum and the properties of the eigenfunctions and the root functions (the smoothness, the completeness and the basis property) (1994–2001). The analysis of the spectral approaches to the construction of the $R$-matrix for the Schrodinger equation and the Dirac system (2001). Collaborated and wrote common papers with the following mathematicians: M. I. Vishik, A. S. Dynin, Z. N. Golubeva, A. S. Markus, B. A. Amosov, M. Faierman, R. Denk, R. Mennicken, M. Levitin. Common book with physicists B. Z. Katsenelenbaum, A. N. Sivov, and N. N. Voitovich. See details in the note in Russian Mathematical Surveys, 2001, 56(4), 163–168. Variational elliptic boundary value problems in Lipschitz domains. Spectral problems. Pseudodifferential operators with nonsmooth symbols or kernels.


Graduated from the Department of Mechanics and Mathematics of Moscow State University in 1953. The M.Sc. thesis was supervised by D. E. Men'shov. In 1953–60, worked as an editor in the Department of Mathematics of the Publishing House of Foreign Literature. Simultaneously, was an external postgraduate student under supervision first by D. E.  Men'shov and later by G. E. Shilov (1954–58). Was the editor of the three well-known books by I. M. Gelfand and G. E. Shilov on generalized functions (1958–59). Defended the Ph.D. thesis in 1959. Since 1961, taught first in All-Union Institute of Mechanical Engineering, since 1962 in Moscow Institute of Electronic Engineering, renamed later Moscow Institute of Electronics and Mathematics (MIEM). Defended the Doctoral Sci. thesis in 1966. Professor since 1970. Head of the Chair of Mathematical Analysis in 1992–98. Member of the Editorial Board of the journal "Functional Analysis and its Applications" since 1967, deputy editor since 1991. Member of the Editorial Board of "Russian Journal of Mathematical Physics" since 1993. After 1989, gave many talks on mathematical seminars and conferences abroad.
A member of the New York Academy of Sciences.

Main publications:
  1. M. C. Agranovich, “Spektralnye zadachi dlya silno ellipticheskikh sistem vtorogo poryadka v oblastyakh s gladkoi i negladkoi granitsei”, UMN, 57:5 (2002), 3–78  mathnet  mathscinet  zmath
  2. M. C. Agranovich, “Operatory tipa potentsiala i zadachi sopryazheniya dlya silno ellipticheskikh sistem 2-go poryadka v oblastyakh s lipshitsevoi granitsei”, Funktsionalnyi analiz i ego prilozheniya, 43:3 (2009), 3–25  mathnet
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. M. S. Agranovich, A. M. Selitskii, “Fractional Powers of Operators Corresponding to Coercive Problems in Lipschitz Domains”, Funktsional. Anal. i Prilozhen., 47:2 (2013),  2–17  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 47:2 (2013), 83–95  isi  elib  scopus
2. M. S. Agranovich, “Spectral problems in Lipschitz domains”, CMFD, 39 (2011),  11–35  mathnet  mathscinet; Journal of Mathematical Sciences, 190:1 (2013), 8–33  scopus
3. M. S. Agranovich, “Mixed Problems in a Lipschitz Domain for Strongly Elliptic Second-Order Systems”, Funktsional. Anal. i Prilozhen., 45:2 (2011),  1–22  mathnet  mathscinet  zmath; Funct. Anal. Appl., 45:2 (2011), 81–98  isi  scopus
4. M. S. Agranovich, “Strongly Elliptic Second-Order Systems with Boundary Conditions on a Nonclosed Lipschitz Surface”, Funktsional. Anal. i Prilozhen., 45:1 (2011),  1–15  mathnet  mathscinet  zmath; Funct. Anal. Appl., 45:1 (2011), 1–12  isi  scopus
5. M. S. Agranovich, “Potential Type Operators and Transmission Problems for Strongly Elliptic Second-Order Systems in Lipschitz Domains”, Funktsional. Anal. i Prilozhen., 43:3 (2009),  3–25  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 43:3 (2009), 165–183  isi  scopus
6. M. S. Agranovich, “Spectral Boundary Value Problems in Lipschitz Domains for Strongly Elliptic Systems in Banach Spaces $H_p^\sigma$ and $B_p^\sigma$”, Funktsional. Anal. i Prilozhen., 42:4 (2008),  2–23  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 42:4 (2008), 249–267  isi  scopus
7. M. S. Agranovich, “To the Theory of the Dirichlet and Neumann Problems for Strongly Elliptic Systems in Lipschitz Domains”, Funktsional. Anal. i Prilozhen., 41:4 (2007),  1–21  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 41:4 (2007), 247–263  isi  scopus
8. M. S. Agranovich, “Regularity of Variational Solutions to Linear Boundary Value Problems in Lipschitz Domains”, Funktsional. Anal. i Prilozhen., 40:4 (2006),  83–103  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 40:4 (2006), 313–329  isi  elib  scopus
9. M. S. Agranovich, G. V. Rozenblum, “Spectral boundary problems for Dirac systems with a singular potential”, Algebra i Analiz, 16:1 (2004),  33–69  mathnet  mathscinet  zmath; St. Petersburg Math. J., 16:1 (2005), 25–57
10. M. S. Agranovich, “Spectral problems for second-order strongly elliptic systems in smooth and non-smooth domains”, Uspekhi Mat. Nauk, 57:5(347) (2002),  3–78  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 57:5 (2002), 847–920  isi  scopus
11. M. S. Agranovich, “Spectral Problems for the Dirac System with Spectral Parameter in Local Boundary Conditions”, Funktsional. Anal. i Prilozhen., 35:3 (2001),  1–18  mathnet  mathscinet  zmath; Funct. Anal. Appl., 35:3 (2001), 161–175  isi  scopus
12. M. S. Agranovich, R. Mennicken, “Spectral boundary value problems for the Helmholtz equation with spectral parameter in boundary conditions on a non-smooth surface”, Mat. Sb., 190:1 (1999),  29–68  mathnet  mathscinet  zmath; Sb. Math., 190:1 (1999), 29–69  isi  scopus
13. M. S. Agranovich, B. A. Amosov, “Estimates of $s$-Numbers and Spectral Asymptotics for Integral Operators of Potential Type on Nonsmooth Surfaces”, Funktsional. Anal. i Prilozhen., 30:2 (1996),  1–18  mathnet  mathscinet  zmath; Funct. Anal. Appl., 30:2 (1996), 75–89  isi
14. M. S. Agranovich, “On Series with Respect to Root Vectors of Operators Associated with Forms Having Symmetric Principal Part”, Funktsional. Anal. i Prilozhen., 28:3 (1994),  1–21  mathnet  mathscinet  zmath; Funct. Anal. Appl., 28:3 (1994), 151–167  isi
15. M. S. Agranovich, “On modules of eigenvalues for non-self-adjoint agmon–Douglis–Nirenberg elliptic boundary problems with a parameter”, Funktsional. Anal. i Prilozhen., 26:2 (1992),  51–55  mathnet  mathscinet  zmath; Funct. Anal. Appl., 26:2 (1992), 116–119  isi
16. M. S. Agranovich, “Non-self-adjoint problems with a parameter that are elliptic in the sense of Agmon–Douglis–Nirenberg”, Funktsional. Anal. i Prilozhen., 24:1 (1990),  59–61  mathnet  mathscinet  zmath; Funct. Anal. Appl., 24:1 (1990), 50–53  isi
17. M. S. Agranovich, “Elliptic operators on closed manifolds”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 63 (1990),  5–129  mathnet  mathscinet  zmath
18. M. S. Agranovich, “Some asymptotic formulas for elliptic pseudodifferential operators”, Funktsional. Anal. i Prilozhen., 21:1 (1987),  63–65  mathnet  mathscinet  zmath; Funct. Anal. Appl., 21:1 (1987), 53–56  isi
19. M. S. Agranovich, “Elliptic pseudodifferential operators on a closed curve”, Tr. Mosk. Mat. Obs., 47 (1984),  22–67  mathnet  mathscinet  zmath
20. M. S. Agranovich, B. A. Amosov, “Elliptic pseudodifferential matrix operators on a closed curve”, Funktsional. Anal. i Prilozhen., 15:3 (1981),  79–81  mathnet  mathscinet  zmath; Funct. Anal. Appl., 15:3 (1981), 217–219  isi
21. M. S. Agranovich, “Convergence of series in root vectors of operators that are nearly selfadjoint”, Tr. Mosk. Mat. Obs., 41 (1980),  163–180  mathnet  mathscinet  zmath
22. M. S. Agranovich, “Spectral properties of elliptic pseudodifferential operators on a closed curve”, Funktsional. Anal. i Prilozhen., 13:4 (1979),  54–56  mathnet  mathscinet  zmath; Funct. Anal. Appl., 13:4 (1979), 279–281
23. M. S. Agranovich, “Series in the root vectors of operators that are very close to being self-adjoint”, Funktsional. Anal. i Prilozhen., 11:4 (1977),  65–67  mathnet  mathscinet  zmath; Funct. Anal. Appl., 11:4 (1977), 296–299
24. M. S. Agranovich, Z. N. Golubeva, “Some problems for Maxwell's system with a spectral parameter in the boundary condition”, Dokl. Akad. Nauk SSSR, 231:4 (1976),  777–780  mathnet  mathscinet  zmath
25. M. S. Agranovich, “Summability of series in root vectors of non-self-adjoint elliptic operators”, Funktsional. Anal. i Prilozhen., 10:3 (1976),  1–12  mathnet  mathscinet  zmath; Funct. Anal. Appl., 10:3 (1976), 165–174
26. M. S. Agranovich, “Theorem on matrices depending on parameters and its applications to hyperbolic systems”, Funktsional. Anal. i Prilozhen., 6:2 (1972),  1–11  mathnet  mathscinet  zmath; Funct. Anal. Appl., 6:2 (1972), 85–93
27. M. S. Agranovich, “Boundary value problems for systems with a parameter”, Mat. Sb. (N.S.), 84(126):1 (1971),  27–65  mathnet  mathscinet  zmath; Math. USSR-Sb., 13:1 (1971), 25–64
28. M. S. Agranovich, “Boundary value problrms for systems of first order pseudodifferential operators”, Uspekhi Mat. Nauk, 24:1(145) (1969),  61–125  mathnet  mathscinet  zmath; Russian Math. Surveys, 24:1 (1969), 59–126
29. M. S. Agranovich, “Positive boundary value problems for pseudodifferential operators of first order”, Funktsional. Anal. i Prilozhen., 2:1 (1968),  90–91  mathnet  mathscinet  zmath; Funct. Anal. Appl., 2:1 (1968), 83–84
30. M. S. Agranovič, “Positive boundary value problems for certain first order systems”, Tr. Mosk. Mat. Obs., 16 (1967),  3–24  mathnet  mathscinet  zmath
31. M. S. Agranovich, V. V. Sukhorutchenko, “The necessity of the algebraic parabolicity conditions of nonstationary problems”, Mat. Zametki, 2:6 (1967),  615–625  mathnet  mathscinet  zmath; Math. Notes, 2:6 (1967), 864–869
32. M. S. Agranovich, “On the theory of boundary problems for symmetrizable systems of first order”, Mat. Sb. (N.S.), 73(115):2 (1967),  161–197  mathnet  mathscinet  zmath; Math. USSR-Sb., 2:2 (1967), 143–171
33. M. S. Agranovich, “Positive mixed problems for certain hyperbolic systems”, Dokl. Akad. Nauk SSSR, 167:6 (1966),  1215–1218  mathnet  mathscinet  zmath
34. M. S. Agranovich, “Elliptic singular integro-differential operators”, Uspekhi Mat. Nauk, 20:5(125) (1965),  3–120  mathnet  mathscinet  zmath; Russian Math. Surveys, 20:5 (1965), 1–121
35. M. S. Agranovich, “General boundary-value problems for integro-differential elliptic systems”, Dokl. Akad. Nauk SSSR, 155:3 (1964),  495–498  mathnet  mathscinet  zmath
36. M. S. Agranovich, M. I. Vishik, “Elliptic problems with a parameter and parabolic problems of general type”, Uspekhi Mat. Nauk, 19:3(117) (1964),  53–161  mathnet  mathscinet  zmath; Russian Math. Surveys, 19:3 (1964), 53–157
37. M. S. Agranovich, M. I. Vishik, “Elliptic boundary-value problems depending on a parameter”, Dokl. Akad. Nauk SSSR, 149:2 (1963),  223–226  mathnet  mathscinet  zmath
38. M. S. Agranovich, M. I. Vishik, “Parabolic boundary-value problems”, Uspekhi Mat. Nauk, 18:1(109) (1963),  206–208  mathnet
39. M. S. Agranovich, A. S. Dynin, “General boundary-value problems for elliptic systems in higher-dimensional regions”, Dokl. Akad. Nauk SSSR, 146:3 (1962),  511–514  mathnet  mathscinet  zmath
40. M. S. Agranovich, “On the problem of the index of elliptic operators”, Dokl. Akad. Nauk SSSR, 142:5 (1962),  983–985  mathnet  mathscinet  zmath
41. M. S. Agranovich, “Partial differential equations with constant coefficients”, Uspekhi Mat. Nauk, 16:2(98) (1961),  27–93  mathnet  mathscinet  zmath; Russian Math. Surveys, 16:2 (1961), 23–90
42. M. S. Agranovich, “General solutions of differential-difference equations with constant coefficients”, Dokl. Akad. Nauk SSSR, 123:1 (1958),  9–12  mathnet  mathscinet  zmath
43. M. S. Agranovich, “Some general formulae for the solution of partial differential equations with constant coefficients”, Izv. Vyssh. Uchebn. Zaved. Mat., 1958, 4,  3–20  mathnet  mathscinet  zmath
44. M. S. Agranovich, “On the consistency of several methods of summation”, Uch. Zap. Mosk. Gos. Univ., 165 (1954),  169–194  mathnet  mathscinet

45. M. S. Agranovich, A. V. Babin, A. S. Demidov, Yu. A. Dubinskii, A. I. Komech, S. B. Kuksin, A. P. Kuleshov, V. P. Maslov, S. P. Novikov, V. M. Tikhomirov, A. V. Fursikov, V. V. Chepyzhov, A. I. Shnirelman, M. A. Shubin, G. I. Eskin, “Marko Iosifovich Vishik (obituary)”, Uspekhi Mat. Nauk, 68:2(410) (2013),  197–200  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 68:2 (2013), 383–387  isi
46. M. S. Agranovich, L. A. Aizenberg, G. L. Alfimov, M. I. Vishik, T. Voronov, A. V. Karabegov, M. V. Karasev, A. A. Komech, V. P. Maslov, V. V. Pukhnachov, D. E. Tamarkin, N. N. Tarkhanov, B. L. Tsygan, M. A. Shubin, “Boris Vasil'evich Fedosov (obituary)”, Uspekhi Mat. Nauk, 67:1(403) (2012),  169–176  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 67:1 (2012), 167–174  isi
47. M. S. Agranovich, I. V. Astashova, L. A. Bagirov, V. V. Vlasov, V. V. Zhikov, Yu. S. Ilyashenko, V. V. Kozlov, A. A. Kon'kov, S. I. Pokhozhaev, E. V. Radkevich, N. Kh. Rozov, I. N. Sergeev, A. L. Skubachevskii, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Vladimir Alexandrovich Kondratiev. July 2, 1935 – March 11, 2010”, CMFD, 39 (2011),  5–10  mathnet  mathscinet; Journal of Mathematical Sciences, 190:1 (2013), 1–7
48. M. S. Agranovich, V. M. Buchstaber, R. S. Ismagilov, B. S. Kashin, B. S. Mityagin, S. P. Novikov, V. A. Sadovnichii, A. G. Sergeev, Ya. G. Sinai, A. A. Shkalikov, “Anatolii Gordeevich Kostyuchenko (obituary)”, Uspekhi Mat. Nauk, 65:4(394) (2010),  179–190  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 65:4 (2010), 767–780  isi  elib
49. M. S. Agranovich, Yu. D. Burago, B. R. Vainberg, M. I. Vishik, S. G. Gindikin, V. A. Kondrat'ev, V. P. Maslov, S. V. Poborchi, Yu. G. Reshetnyak, V. P. Khavin, M. A. Shubin, “Vladimir Gilelevich Maz'ya (to his 70th brithday)”, Uspekhi Mat. Nauk, 63:1(379) (2008),  183–189  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 63:1 (2008), 189–196  isi
50. M. S. Agranovich, A. I. Aptekarev, A. L. Afendikov, N. D. Vvedenskaya, M. I. Vishik, S. G. Gindikin, M. M. Malamud, B. P. Paneah, E. V. Radkevich, V. M. Tikhomirov, A. R. Shirikyan, “Leonid Romanovich Volevich (obituary)”, Uspekhi Mat. Nauk, 62:6(378) (2007),  157–160  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 62:6 (2007), 1187–1190  isi
51. M. S. Agranovich, A. I. Aptekarev, N. D. Vvedenskaya, M. I. Vishik, S. G. Gindikin, A. M. Il'in, V. P. Maslov, M. M. Malamud, B. P. Paneah, V. M. Tikhomirov, A. R. Shirikyan, “Leonid Romanovich Volevich (on his 70th birthday)”, Uspekhi Mat. Nauk, 59:5(359) (2004),  175–182  mathnet  mathscinet  zmath; Russian Math. Surveys, 59:5 (2004), 991–1000  isi
52. M. S. Agranovich, V. I. Arnol'd, D. G. Vasil'ev, M. I. Vishik, I. M. Gel'fand, A. G. Kostyuchenko, L. D. Kudryavtsev, “Victor Borisovich Lidskii (on his 75th birthday)”, Uspekhi Mat. Nauk, 54:5(329) (1999),  197–203  mathnet  mathscinet  zmath; Russian Math. Surveys, 54:5 (1999), 1077–1085  isi
53. M. S. Agranovich, A. V. Babin, L. R. Volevich, A. Yu. Goritskii, A. S. Demidov, Yu. A. Dubinskii, A. I. Komech, M. L. Krasnov, S. B. Kuksin, G. I. Makarenko, V. P. Maslov, V. M. Tikhomirov, A. V. Fursikov, V. V. Chepyzhov, A. I. Shnirel'man, M. A. Shubin, “Mark Iosifovich Vishik (on his 75th birthday)”, Uspekhi Mat. Nauk, 52:4(316) (1997),  225–232  mathnet  mathscinet  zmath; Russian Math. Surveys, 52:4 (1997), 853–861  isi
54. M. S. Agranovich, I. M. Gel'fand, Yu. A. Dubinskii, O. A. Oleinik, S. L. Sobolev, M. A. Shubin, “Mark Iosifovich Vishik (on his sixtieth birthday)”, Uspekhi Mat. Nauk, 37:4(226) (1982),  213–220  mathnet  mathscinet  zmath; Russian Math. Surveys, 37:4 (1982), 175–184  isi

Presentations in Math-Net.Ru
1. 90-летию со дня рождения выдающегося математика Марка Иосифовича Вишика посвящается
V. M. Tikhomirov, M. S. Agranovich, Yu. A. Dubinskii, A. V. Fursikov, V. V. Chepyzhov
Meetings of the Moscow Mathematical Society
October 25, 2011 18:30
2. Mixed problems and crack-type problems for strongly elliptic second-order systems in domains with Lipschitz boundaries
M. S. Agranovich
Sixth International Conference on Differential and Functional Differential Equations DFDE-2011
August 19, 2011 12:00   

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