Vol'pert developed an effective algorithm for calculating the index of an elliptic problem before the Atiyah-Singer index theorem appeared: He was also the first to show that the index of a singular matrix operator can be different from zero.
He was one of the leading contributors to the theory of BV-functions: he introduced the concept of functional superposition, which enabled him to construct a calculus for such functions and applying it in the theory of partial differential equations. Precisely, given a continuously differentiable function and a function of bounded variation with and, he proves that is again a function of bounded variation and the following chain ruleformula holds: where is the already cited functional superposition of and. By using his results, it is easy to prove that functions of bounded variation form an algebra of discontinuous functions: in particular, using his calculus for, it is possible to define the product of the Heaviside step function and the Dirac distribution in one variable.
. A seminal paper where Caccioppoli sets and BV functions are thoroughly studied and the concept of functional superposition is introduced and applied to the theory of partial differential equations: it was also translated as.
. A short announce of the "Partial Differential Equations and Applications" conference in celebration of Aizik I. Volpert's 80th Birthday, held in June 2003 by the Center for Mathematical Sciences, including a few biographical details. The conference participants and program can be found at the conference web site.
. The "Mathematics in the USSR 1958–1967" is a two–volume continuation of the opus "Mathematics in the USSR during its first forty years 1917–1957" and describes the developments of Soviet mathematics during the period 1958–1967. Precisely it is meant as a continuation of the second volume of that work and, as such, is titled "Biobibliography". It includes new biographies and bibliographies of works published by new Soviet mathematicians during that period, and updates on the work and biographies of scientist included in the former volume, alphabetically ordered with respect to author's surname.
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. "Mathematics in the USSR during its first forty years 1917–1957 is an opus in two volumes describing the developments of Soviet mathematics during the first forty years of its existence. This is the second volume, titled "Biobibliography", containing a complete bibliography of works published by Soviet mathematicians during that period, alphabetically ordered with respect to author's surname and including, when possible, brief but complete biographies of the authors.
. "Institute of Problems of Chemical Physics. Fifty years in the trenches" is a brief historical sketch of the institute, published in the first volume of the 2004 yearbook.
Scientific references
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. "Mathematics in the USSR during its first forty years 1917–1957 is an opus in two volumes describing the developments of Soviet mathematics during the first forty years of its existence. This is the first volume, titled "Survey articles" and consists exactly of such kind of articles authored by Soviet experts and reviewing briefly the contributions of Soviet mathematicians to a chosen field, during the years from 1917 to 1957.
