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Register a new userBoris R. Vainberg (on his 80th birthday)
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Evgeny Lakshtanov L
Publication date
2018
fields
Physics
and research's language is
English
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No Arabic abstract
Boris R. Vainberg was born on March 17, 1938, in Moscow. His father was a Lead Engineer in an aviation design institute. His mother was a homemaker. From early age, Boris was attracted to mathematics and spent much of his time at home and in school working through collections of practice problems for the Moscow Mathematical Olympiad. His first mathematical library consisted of the books he received as one of the prize-winners of these olympiads.
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This article is a collection of several memories for a special issue of SIGMA devoted to Dmitry Borisovich Fuchs.
This paper appeals to the figure of Evariste Galois for investigating the gates between mathematics and their publics. The figure of Galois draws some lines of/within mathematics for/from the outside of mathematics and these lines in turn sketch the silhouette of Galois as a historical figure. The present paper especially investigates the collective categories that have been used in various types of public discourses on Galoiss work (e.g. equations, groups, algebra, analysis, France, Germany etc.). In a way, this paper aims at shedding light on the boundaries some individuals drew by getting Galois his gun. It is our aim to highlight the roles of authority some individuals (such as as Picard) took on in regard with the public figure of Galois as well as the roles such authorities assigned to other individuals (such as the mediating role assigned to Jordan as a mediator between Galoiss ideas and the public). The boundary-works involved by most public references to Galois have underlying them a long-term tension between academic and public legitimacies in the definition of some models for mathematical lives (or mathematics personae)
This article discusses the life and work of Professor Ola Bratteli (1946--2015). Family, fellow students, his advisor, colleagues and coworkers review aspects of his life and his outstanding mathematical accomplishments.
In this paper the spectral and scattering properties of a family of self-adjoint Dirac operators in $L^2(Omega; mathbb{C}^4)$, where $Omega subset mathbb{R}^3$ is either a bounded or an unbounded domain with a compact $C^2$-smooth boundary, are studied in a systematic way. These operators can be viewed as the natural relativistic counterpart of Laplacians with Robin boundary conditions. Among the Dirac operators treated here is also the so-called MIT bag operator, which has been used by physicists and more recently was discussed in the mathematical literature. Our approach is based on abstract boundary triple techniques from extension theory of symmetric operators and a thorough study of certain classes of (boundary) integral operators, that appear in a Krein-type resolvent formula. The analysis of the perturbation term in this formula leads to a description of the spectrum and a Birman-Schwinger principle, a qualitative understanding of the scattering properties in the case that $Omega$ is unbounded, and corresponding trace formulas.
In this article Dirac operators $A_{eta, tau}$ coupled with combinations of electrostatic and Lorentz scalar $delta$-shell interactions of constant strength $eta$ and $tau$, respectively, supported on compact surfaces $Sigma subset mathbb{R}^3$ are studied. In the rigorous definition of these operators the $delta$-potentials are modelled by coupling conditions at $Sigma$. In the proof of the self-adjointness of $A_{eta, tau}$ a Krein-type resolvent formula and a Birman-Schwinger principle are obtained. With their help a detailed study of the qualitative spectral properties of $A_{eta, tau}$ is possible. In particular, the essential spectrum of $A_{eta, tau}$ is determined, it is shown that at most finitely many discrete eigenvalues can appear, and several symmetry relations in the point spectrum are obtained. Moreover, the nonrelativistic limit of $A_{eta, tau}$ is computed and it is discussed that for some special interaction strengths $A_{eta, tau}$ is decoupled to two operators acting in the domains with the common boundary $Sigma$.
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