Boris Rufimovich Vainberg

Boris Rufimovich Vainberg was born on 17 March 1938 in Moscow. His father was a leading engineer at an aircraft design office and his mother was a housewife. From his early years Boris was interested in mathematics, took part in mathematical study groups (very popular at that time), and participated in the regularly held Moscow mathematical olympiads. His first mathematics library consisted of the books he received as prizes won in olympiads. On graduating from secondary school, Boris enrolled in 1955 in the Faculty of Mechanics and Mathematics (Mech-Math) of Moscow State University, and in 1960, after the usual 5-year course, he began postgraduate studies in the Department of Differential Equations, where Professor S.A. Gal’pern was his scientific advisor. At that time the department was led by Ivan Georgievich Petrovsky, the rector of Moscow University, who was an embodiment of what we can now call ‘the golden age of ‘Mech-Math’. Such prominent researchers as V. I. Arnold, M. I. Vishik, E. M. Landis, and O.A. Oleinik were teaching then in the department. Other departments also featured such star researchers as A. N. Kolmogorov (probability theory), P. S. Alexandroff (topology), I. M. Gelfand and D. E. Men’shov (theory of functions and functional analysis), . . . ; the list goes on and on. At these times of a political ‘thaw’ Mech-Math and particularly its Department of Differential Equations were very responsive to the very latest scientific ideas. First and foremost was the theory of distributions, founded by S. L. Sobolev as long ago as the 1930s, extended by L. Schwartz in the 1950s, and then further developed by Gelfand, G. E. Shilov, and others. Here we should also mention L. Hörmander’s revolutionary works (on pseudodifferential operators, integral Fourier operators, hypoelliptic operators). One of Vainberg’s important publications at the beginning of his career in research was devoted precisely to an analysis

[1]  B. Vainberg,et al.  Spectrum of Multidimensional Schrödinger Operators with Sparse Potentials , 2019, Analytical and computational methods in scattering and applied mathematics.

[2]  E. Lakshtanov,et al.  Solution of the initial value problem for the focusing Davey-Stewartson II system , 2016, Contemporary Mathematics.

[3]  B. Vainberg,et al.  Spectral analysis of non-local Schrödinger operators , 2016, 1603.01626.

[4]  E. Lakshtanov,et al.  On reconstruction of complex-valued once differentiable conductivities , 2015, 1511.08780.

[5]  E. Lakshtanov,et al.  A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy , 2015, 1509.06495.

[6]  B. Vainberg,et al.  Intermittency for branching walks with heavy tails , 2015, 1509.02214.

[7]  E. Lakshtanov,et al.  Recovery of interior eigenvalues from reduced near field data , 2015, 1501.03748.

[8]  Evgeny Lakshtanov,et al.  Sharp Weyl Law for Signed Counting Function of Positive Interior Transmission Eigenvalues , 2014, SIAM J. Math. Anal..

[9]  B. Vainberg,et al.  On mathematical foundation of the Brownian motor theory , 2013, 1304.6790.

[10]  E. Lakshtanov,et al.  Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem , 2012, 1212.6785.

[11]  B. Vainberg,et al.  On the negative spectrum of the hierarchical Schrödinger operator , 2012, 1206.4019.

[12]  B. Vainberg,et al.  Bargmann type estimates of the counting function for general Schrödinger operators , 2012, 1201.3135.

[13]  Yuri A. Godin,et al.  Lyapunov exponent of the random Schrödinger operator with short-range correlated noise potential , 2011, 1104.3150.

[14]  Yuri A. Godin,et al.  The effect of disorder on the wave propagation in one-dimensional periodic optical systems , 2011, 1110.4132.

[15]  B. Vainberg,et al.  Scattering of solitons for coupled wave-particle equations , 2010, Journal of mathematical analysis and applications.

[16]  B. Vainberg,et al.  Non-random perturbations of the Anderson Hamiltonian , 2010, 1002.4220.

[17]  홍대기,et al.  Wave propagation in periodic networks of thin fibers , 2009, 0908.0156.

[18]  M. Cranston,et al.  Continuous Model for Homopolymers , 2009, 0902.2830.

[19]  B. Vainberg,et al.  Propagation of Waves in Networks of Thin Fibers , 2009, 0902.1567.

[20]  B. Vainberg,et al.  Laplace Operator in Networks of Thin Fibers: Spectrum Near the Threshold , 2007, 0704.2795.

[21]  B. Vainberg,et al.  Scattering Solutions in Networks of Thin Fibers: Small Diameter Asymptotics , 2006, math-ph/0609021.

[22]  B. Vainberg,et al.  Schrödinger operators with matrix potentials. Transition from the absolutely continuous to the singular spectrum , 2003, math-ph/0308012.

[23]  B. Vainberg,et al.  Radiation conditions for the difference schrödinger operators , 2001 .

[24]  P. Kuchment,et al.  On absence of embedded eigenvalues for schrÖdinger operators with perturbed periodic potentials , 1999, math-ph/9904016.

[25]  B. Vainberg,et al.  Scattering on the system of the sparse bumps: multidimensional case , 1998 .

[26]  B. Vainberg,et al.  On Spectral Asymptotics for Domains with Fractal Boundaries of Cabbage Type , 1998 .

[27]  Alexander Komech,et al.  On asymptotic stability of stationary solutions to nonlinear wave and Klein-Gordon equations , 1996 .

[28]  M. Cranston,et al.  A solvable model for homopolymers and self-similarity near the critical point , 2010 .

[29]  A. Laptev.  Around the Research of Vladimir Maz'ya III , 2010 .

[30]  P. Ricci,et al.  Analysis, Partial Differential Equations and Applications , 2009 .

[31]  B. Vainberg,et al.  First KdV Integrals¶and Absolutely Continuous Spectrum¶for 1-D Schrödinger Operator , 2001 .

[32]  B. Vainberg,et al.  On spectral asymptotics for domains with fractal boundaries , 1997 .

[33]  B. Vainberg.  Scattering of waves in a medium depending periodically on time , 1992 .