Mikhail Aleksandrovich Shubin

Abstract

The prominent mathematician Mikhail Aleksandrovich Shubin passed away after a long illness on 13 May 2020. He was born on 19 December 1944 in Kuibyshev (now Samara) and raised by his mother and grandmother. His mother, Maria Arkadievna, was an engineer at the State Bearing Factory, where she was hired in 1941 after graduating from the Faculty of Mechanics and Mathematics at the Moscow State University. At that time the factory was evacuated from Moscow to Kuibyshev. She worked at the factory for many years as the Head of the Physics of Metals Laboratory. Later, she defended her Ph.D. thesis and moved to Kuibyshev Polytechnical Institute, where she worked as an associate professor. In his school years Shubin was mainly interested in music. He had absolute pitch. After finishing music school, he seriously considered entering a conservatory. However, in high school he developed an interest to mathematics, was successful in olympiads, and eventually decided to apply to the Faculty of Mechanics and Mathematics at the Moscow State University. He was admitted there in 1961. When the time came to choose an adviser, he became a student of M. I. Vishik. After graduating, he began postgraduate work there, and in 1969 defended his Ph.D. thesis. In the thesis he derived formulae for the index of matrix-valued Wiener–Hopf operators. In particular, for the study of families of such operators, he had to generalize a theorem of Birkhoff stating that a continuous matrix-valued function M(z) defined on the unit circle |z| = 1 can be factored as M(z) = A+(z)D(z)A−(z), where A+(z) and A−(z) are continuous and have analytic continuations to the interior of the unit circle and its exterior (infinity included), respectively, and D(z) is a diagonal matrix with entries zj on the diagonal, with integer nj . Shubin considered the problem of what happens when the matrix M depends continuously on an additional parameter t. The Birkhoff factorization cannot be made continuous