Explore: Pontri͡agin Spaces

{\displaystyle J} -space) if ( x , y ) {\displaystyle (x,\,y)} is positive definite and K {\displaystyle K} possesses a majorant topology. Krein spaces are named

in operator theory there are specific instances of Krein spaces called Pontryagin spaces. Starting in 1952, he worked in optimal control theory. His

barreled spaces (in particular, to all Fréchet spaces). In the 1990s Sergei Akbarov gave a description of the class of the topological vector spaces that

analysis notions such as the Fourier transform and L p {\displaystyle L^{p}} spaces can be generalized. Many of the results of finite group representation theory

example, in physics, configuration spaces or phase spaces). The coordinates of a point r in an n-dimensional space are simply an ordered set of n numbers:

f(|x|)P(x) where P(x) is in Ak. The space L2(Rn) is then a direct sum of the spaces Hk and the Fourier transform maps each space Hk to itself and is possible

Among his teachers there were A. N. Kolmogorov, I. M. Gelfand, L. S. Pontriagin and Pavel Alexandrov. While a student of Andrey Kolmogorov at Moscow State