On M. G. Krein's contribution to the moment problem (Q1899474)

The author gives a survey of scientific results of the famous mathematician M. G. Krein connected with his contribution to the moment problem. The paper contains 6 sections and detailed references of his works and related topics. The author discusses Krein's results starting from his first works with N. Akhiezer in 1934-1938 that were devoted to the problems connected with Fourier coefficients of bounded real functions. Further, Krein's results in the framework of another approach, the theory of canonical solutions and ``limiting values'' of integrals are given, the generalization of the results of the St. Petersburg School is presented. The author discusses in detail other of their joint results in the theory of ``limiting integrals'' and surveys Krein's results in the \(L\)-problem in abstract linear normed spaces, in continuative analog of the trigonometric and power moment problems and also announces some applications to his mechanical interpretation of Stieltjes' investigation of the moment problem and continued fractions.