1. Solomon Grigor'evich Mikhlin was a Soviet mathematician of who worked in the fields of linear elasticity, singular integrals and numerical analysis: he is best known for the introduction of the symbol of a singular integral operator, which eventually led to the foundation and development of the theory of pseudodifferential operators.
Solomon Mikhlin was born in Kholmech, Rechytsa District, Minsk Governorate on 23 April 1908; Mikhlin himself states in his resume that his father was a merchant, but this assertion could be untrue since, in that period, people sometimes lied on the profession of parents in order to overcome political limitations in the access to higher education.
Solomon Mikhlin died of peritonitis in 1961 during a boat trip on Volga.
Solomon Mikhlin's second wife was Eugenia Yakovlevna Rubinova, born in 1918, who was his companion for the rest of his life.
Solomon Mikhlin graduated from a secondary school in Gomel in 1923 and entered the State Herzen Pedagogical Institute in 1925.
Solomon Mikhlin received the order of the Badge of Honour in 1961: the name of the recipients of this prize was usually published in newspapers.
Solomon Mikhlin was awarded of the Laurea honoris causa by the Karl-Marx-Stadt Polytechnic in 1968 and was elected member of the German Academy of Sciences Leopoldina in 1970 and of the Accademia Nazionale dei Lincei in 1981.
Solomon Mikhlin lived in one of the most difficult periods of contemporary Russian history.
However, Solomon Mikhlin was not allowed to visit Italy by the Soviet authorities, so Fichera and his wife brought the tiny golden lynx, the symbol of the Lincei membership, directly to Solomon Mikhlin's apartment in Leningrad on 17 October 1981: the only guests to that "ceremony" were Vladimir Maz'ya and his wife Tatyana Shaposhnikova.
Solomon Mikhlin was author of monographs and textbooks which become classics for their style.
Solomon Mikhlin's research is devoted mainly to the following fields.
In mathematical elasticity theory, Solomon Mikhlin was concerned by three themes: the plane problem, the theory of shells and the Cosserat spectrum.
Solomon Mikhlin studied its convergence and gave applications to special applied problems.
Solomon Mikhlin proved existence theorems for the fundamental problems of plane elasticity involving inhomogeneous anisotropic media: these results are collected in the book.
Solomon Mikhlin studied the error of the approximate solution for shells, similar to plane plates, and found out that this error is small for the so-called purely rotational state of stress.
Solomon Mikhlin proved a theorem on perturbations of positive operators in a Hilbert space which let him to obtain an error estimate for the problem of approximating a sloping shell by a plane plate.
Solomon Mikhlin is one of the founders of the multi-dimensional theory of singular integrals, jointly with Francesco Tricomi and Georges Giraud, and one of the main contributors.
Solomon Mikhlin was the first to develop a theory of singular integral equations as a theory of operator equations in function spaces.
Solomon Mikhlin proved the Fredholm's theorems for singular integral equations and systems of such equations under the hypothesis of non-degeneracy of the symbol: he proved that the index of a single singular integral equation in the euclidean space is zero.
In 1961 Solomon Mikhlin developed a theory of multidimensional singular integral equations on Lipschitz spaces.
Solomon Mikhlin proved a now classical theorem on multipliers of Fourier transform in the L-space, based on an analogous theorem of Jozef Marcinkiewicz on Fourier series.
In 1951 Solomon Mikhlin proved the convergence of the Schwarz alternating method for second order elliptic equations.
Solomon Mikhlin applied the methods of functional analysis, at the same time as Mark Vishik but independently of him, to the investigation of boundary value problems for degenerate second order elliptic partial differential equations.
Solomon Mikhlin studied the completeness of the coordinate functions used in this methods in the Sobolev space, deriving the order of approximation as a function of the smoothness properties of the functions to be approximation of functions approximated.
Solomon Mikhlin characterized the class of coordinate functions which give the best order of approximation, and has studied the stability of the variational-difference process and the growth of the condition number of the variation-difference matrix.
Solomon Mikhlin studied the finite element approximation in weighted Sobolev spaces related to the numerical solution of degenerate elliptic equations.
Solomon Mikhlin found the optimal order of approximation for some methods of solution of variational inequalities.
Solomon Mikhlin was the "kandidat nauk" advisor of Tatyana O Shaposhnikova.
Solomon Mikhlin was mentor and friend of Vladimir Maz'ya: he was never his official supervisor, but his friendship with the young undergraduate Maz'ya had a great influence on shaping his mathematical style.