Grigori Rozenblum

grigorirozenblioum

Professor, PhD, associate professor (Russia),
Professor (Sweden)

email: grigoriblum@gmail.com

PURE SPBU

Research interests:

  1. Spectral theory of differential and integral operators,
  2. Toeplitz operators

Main papers (> 75 in total)

  1. Distribution of the discrete spectrum of singular differential operators. (Russian) Dokl. Akad. Nauk SSSR 202 (1972), 1012–1015.
  2. Near-similarity of operators and the spectral asymptotic behavior of pseudodifferential operators on the circle. (Russian) Trudy Moskov. Mat. Obshch. 36 (1978), 59–84,
  3. Spectral asymptotic behavior of elliptic systems. (Russian) Boundary value problems of mathematical physics and related questions in the theory of functions, 12. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 96 (1980), 255–271 (with Solomyak, M. Z.; Shubin, M. A.)
  4. Spectral theory of differential operators. (Russian) Current problems in mathematics. Fundamental directions, Vol. 64 (Russian), 5–248, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1989; English translation: Springer, Encyclopaedia of Mathematical Sciences , vol.64, 1994
  5. Index formulae for pseudodifferential operators with discontinuous symbols. Ann. Global Anal. Geom. 15 (1997), no. 1, 71–100. Domination of semigroups and estimates for eigenvalues. (Russian) Algebra i Analiz 12 (2000), no. 5, 158—177 ( with Melgaard, M.)
  6. Eigenvalue asymptotics for weakly perturbed Dirac and Schrödinger operators with constant magnetic fields of full rank. Comm. Partial Differential Equations 28 (2003), no. 3-4, 697–736.
  7. Regularisation of secondary characteristic classes and unusual index formulas for operator-valued symbols. Nonlinear hyperbolic equations, spectral theory, and wavelet transformations, 419–437, Oper. Theory Adv. Appl., 145, Adv. Partial Differ. Equ. (Basel), Birkhäuser, Basel, 2003. ( with Agranovich, M. S.);
  8. Spectral boundary value problems for a Dirac system with singular potential. (Russian) Algebra i Analiz 16 (2004), no. 1, 33—69; ( with Melgaard, M. )
  9. Schrödinger operators with singular potentials. Stationary partial differential equations. Vol. II, 407–517, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, 2005. (with Shirokov, N.)
  10. Infiniteness of zero modes for the Pauli operator with singular magnetic field. J. Funct. Anal. 233 (2006), no. 1, 135–172. ( with Tashchiyan, G.)
  11. On the spectral properties of the perturbed Landau Hamiltonian. Comm. Partial Differential Equations 33 (2008), no. 4-6, 1048–1081. ( with Sobolev, Alexander V).
  12. Discrete spectrum distribution of the Landau operator perturbed by an expanding electric potential. Spectral theory of differential operators, 169–190, Amer. Math. Soc. Transl. Ser. 2, 225, Adv. Math. Sci., 62, Amer. Math. Soc., Providence, RI, 2008.
  13. On lower eigenvalue bounds for Toeplitz operators with radial symbols in Bergman spaces. J. Spectr. Theory 1 (2011), no. 3, 299–325. (with Vasilevski, N.)
  14. Toeplitz operators defined by sesquilinear forms: Fock space case. J. Funct. Anal. 267 (2014), no. 11, 4399–4430. (with Shirokov, N. ) Some weighted estimates for the ∂¯¯¯-equation and a finite rank theorem for Toeplitz operators in the Fock space. Proc. Lond. Math. Soc. (3) 109 (2014), no. 5, 1281–1303. (with Vasilevski, N.)
  15. Toeplitz operators in the Herglotz space. Integral Equations Operator Theory 86 (2016), no. 3, 409–438. (with Nursultanov, M.)
  16. Eigenvalue asymptotics for the Sturm-Liouville operator with potential having a strong local negative singularity. Opuscula Math. 37 (2017), no. 1, 109–139. ( with Tashchiyan, G) .
  17. Eigenvalue asymptotics for potential type operators on Lipschitz surfaces of codimension greater than 1. Opuscula Math. 38 (2018), no. 5, 733–758.

Teaching:

  1. Methods of investigation of discrete spectrum for operators of mathematical physics, Master students

Other information:

  1. Editor in Chief: American Journal of Mathematical Analysis
  2. Member of editorial board: Journal of Spectral Theory
  3. Member of editorial board: Boletín de la Sociedad Matemática Mexicana Journal of Mathematical Sciences (Springer)

Mikhail I. Belishev

Professor, Doctor of Sciences

DSC_9790

email: belishev@pdmi.ras.ru
PURE СПбГУ

Full-time job

St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences, Laboratory of Mathematical Problems of Geophysics.

Specialization:

inverse problems of mathematical physics.
In particular, 

  • multidimensional time-domain and frequency-domain coefficient inverse problems;
  • reconstruction of Riemannian manifolds via the boundary data;
  • inverse problems for the vectorial dynamical systems;
  • forward and inverse problems on graphs;
  • mathematical control theory problems.

 Directions of research

  • inverse problem theory;
  • control and system theory;
  • partial differential equations;
  • asymptotic methods in mathematical physics;
  • function analysis and operator theory.

Prospective goals:

  • relations between inverse problems and C*-algebras and noncommutative geometry;
  • function models of linear operators;
  • inverse problems for multichannel dynamical systems.

Basic Research papers

  1. Infringement of the condition for solvability of the converse problem for an inhomogeneous string
  2. Boundary control in reconstruction of manifolds and metrics (the BC method)
  3. Characterization of Data of the Dynamical Inverse Problem for a Two-Velocity System
  4. Boundary Control Method and Inverse Problems of Wave Propagation
  5. Boundary spectral inverse problem on a class of graphs (trees) by the BC method
  6. Some remarks on the impedance tomography problem for 3d–manifolds.
  7. Recent progress in the boundary control method
  8. Dirichlet to Neumann operator on differential form
  9. s-POINTS IN THREE-DIMENSIONAL ACOUSTICAL SCATTERING
  10. A UNITARY INVARIANT OF A SEMI-BOUNDED OPERATOR IN RECONSTRUCTION OF MANIFOLDS
  11. Elements of noncommutative geometry in inverse problems on manifolds

Alexander M. Budylin

DSC_9774

Associate professor, PhD

 

email: A.M.Budylin (official)
email: budylin@math.nw.ru

Students’ pages are here and here

PURE SPBU

Directions of research

  • Semiclassical asymptotics
  • Pseudodifferential equations
  • Spectral theory

Basic research papers

  1. On the asymptotic behavior of spectral characteristics of an integral operator with difference kernel on expanding regions (with Buslaev V.S.)
    1986, Soviet Math.Dokl., vol.33, \No 2, p.400-403 .
  2. Reflection operators and their applications to asymptotic investigations of semiclassical integral equations. (With Buslaev V.S.)
    1991, Advances in Soviet Math., AMS, Providence, vol. 7, p.107-157 .
  3. Semiclassical asymptotics of the resolvent of the integral convolution operator with the sine-kernel on a finite interval. (With Buslaev V.S.)
    1996, St.Petersburg Math.J., vol.7, \No 6, p.925-942 .
  4. Semiclassical pseudodifferential operators with double discontinuous symbols and their application to the problems of quantum statistical physics. (With Buslaev V.S.)
    2001, Operator Theory: Advances and Aplications, v.126.
  5. Quasiclassical asymptotics for solutions of the matrix conjugation problem with rapid oscillation of off-diagonal entries. 2014, St. Petersburg mathematical journal, vol. 25, n.2, pp. 205-222.

 

Teaching

  • Lectures «Higher mathematics» for 2nd year students, General stream
  • Seminars «Higher mathematics» for 2nd year students
  • Seminars «Group theory» for 4th year students (Department of higher mathematics and mathematical physics)
  • Lectures «Theory of Lie groups and Lie algebras» for 4th year students (Department of higher mathematics and mathematical physics)
  • Seminars «Theory of Lie groups and Lie algebras» for 4th year students (Department of higher mathematics and mathematical physics)
  • Seminars «History and methodology of mathematical physics» for 5th year students (Department of higher mathematics and mathematical physics)

 

Киселёв Алексей Прохорович

профессор, доктор ф.-м. наук

Киселев Алексей Прохорович

email: kiselev@pdmi.ras.ru

Домашняя страница здесь

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Научные интересы

  • Дифракция и распространение волн
  • Приложения к механике, оптике, акустике Читать далее

Коротяев Евгений Леонидович

korot

профессор, доктор физико-математических наук

email:korotyaev@gmail.com

Страница на Google Scholar

Fields of Research

  • 1D inverse spectral theory for Schrodinger operator with periodic potentials, Sturm-Liouville problems on finite intervals, for the difference operators, Schrodinger operator with matrix-valued potentials, perturbed harmonic oscillator.
  • Integrable systems (KdV and non-linear Schrodinger equation), a priori estimates for integrable systems, symplectic coordinates.
  • Geometric function theory (harmonic and functional analysis, geometric function theory, the Lowner equation for the conformal mapping associated with quasimomentum)
  • Scattering theory including few body systems in external fields.
  • Schrodinger operators on periodic media, including graphs, and nano-media.
  • Theory of resonances and inverse resonance scattering.
  • Multidimensional inverse problems for Schrodinger operators on the lattice. Читать далее

Mikhail A. Lyalinov

Professor, Doctor of Sciences

DSC_9786

email: lyalinov@yandex.ru
PURE SPBU

 Directions of research

  • Asymptotic methods for the boundary-value problems of the wave propagation theory
    (acoustic, electromagnetic waves and gravity surface waves)
  • Mathematical theory of diffraction and canonical problems (formulas, integral transforms, functional equations, asymptotic estimates of the integral representations, numerical simulation)

Basic Research papers

  1. Mikhail A. Lyalinov, Electromagnetic scattering by a circular impedance cone: diffraction coefficients and surface waves, IMA Journal of Applied Mathematics (2014), P. 1 – 38  ( doi:10.1093/imamat/hxs072, to appear).
  2. Mikhail A. Lyalinov , Scattering of acoustic waves by a sector, Wave Motion 50 (2013) 739–762.
  3. Mikhail A. Lyalinov and Ning Yan Zhu, Electromagnetic Scattering of a Dipole-Field by an Impedance Wedge, Part I: Far-Field Space Waves, IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 1, JANUARY (2013), 329-336.

Monographs

  1. V. M. Babich, M. A. Lyalinov and V. E. Grikurov, Diffraction Theory:
    the Sommerfeld-Malyuzhinets Technique (Alpha Science Series on Wave
    Phenomena). Oxford, UK: Alpha Science, 2008.
  2. M.A. Lyalinov, N.Y. Zhu, Scattering of Waves by Wedges and Cones with Impedance Boundary Conditions, in: Mario Boella Series on Electromagnetism in Information & Communication, SciTech-IET, Edison, NJ, 2012.

Research projects for students

  1. Mathematical modeling of the initial stage of initial stage of the tsunami- wave
    (linear approximation of the shallow water, integral transforms, functional equations,
    separation of the variables, asymptotic analysis)
  2. Electromagnetic scattering of surface wave by the geometrical discontinuities of the boundary, applications to the study to the scattering of surface polaritons

Сарафанов Олег Васильевич

профессор, доктор физико-математических наук

sarafanov

email: osarafanov@rambler.ru

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Научные интересы

  • псевдодифференциальные операторы и краевые задачи в областях с особенностями

Boris A. Plamenevskii

Professor, Doctor of Sciences

ПламеневскийБА_1

email: boris.plamen@gmail.com b.plamenevskii@spbu.ru
PURE SPBU

Research work

Approximately 170 publications including several monographs.

The studies are devoted to

  • the theory of elliptic boundary value problems for partial differential equations,
  • pseudo-differential operators,
  • mathematical waveguide theory with applications to electrodynamics, hydrodynamics, elasticity theory, and electronics.

Main monographs

  1. B.A.Plamenevskii, Algebras of Pseudodifferetial Operators, M., Nauka, 1986 (in Russian)
    Plamenevskii B.A., Algebras of Pseudodifferential Operators, Nauka, Kluver Academic Press, Dordrecht/Boston/London, 1989.(English Translation).
  2. S.A.Nazarov, B.A.Plamenevskii, Elliptic Problems in Domains with Piecewise Smooth Boundaries, M., Nauka, 1991 (in Russian).
    Nazarov S.A. and Plamenevski B.A., Elliptic Problems in Domains with Piecewise Smooth Boundaries, Berlin; New-York: De Gruyter, 1994 (Extended version, in English).
  3. V.Maz’ya, S.Nazarov, B.Plamenevskii, Asymptotische Theorie Elliptischer Rahdwertaufgaben in Singular Gestorten Gebieten, b.1, 2, Academic Verlag, Berlin, 1991 (in German).
    V.Maz’ya, S.Nazarov, B.Plamenevskii, Asymptotic Theory of Elliptic Problems in Singularly Perturbed Domains, vol. 1, 2, Birkhauser, 2000, (Operator Theory, Advances and Applications, v.111, 112) (English translation).
  4. B.A.Plamenevskii, Pseudodifferential Operators on Piecewise Smooth Manifolds, Novosibirsk, «Tamara Rozhkovskaya», 2010 (in Russian).
  5. L.Baskin, P.Neittaanmaki, B.Plamenevskii, O.Sarafanov, Resonant Tunneling (Subtitle: Quantum Waveguides of Variable Cross-Sections, Asymptotics, Numerics and Applications), Springer, 2015 (in English).

Teaching activity

Lectures:

  1. «Calculus» (for the 1st year students)
  2. «The geometry of manifolds» (for the 3rd year students)
  3. «Boundary value problems and pseudodifferential operators» (for graduate and post-graduate students)

Scientific supervisor of undergraduate, graduate and post-graduate students

Alexander A. Fedotov

fedotov
professor, Doctor of Sciences
email: fedotov.s@mail.ru a.fedotov@spbu.ru
PURE SPBU

 Directions of research

  • Asymptotic methods of mathematical physics (quasi-classical, short-wave and adiabatic asymptotics)
  • Spectral theory of ergodic Schr\»odinger operators
  • Analytic theory of difference equations on the complex plane

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