HANKEL OPERATORS OF CLASS $ \mathfrak{S}_p$ AND THEIR APPLICATIONS (RATIONAL APPROXIMATION, GAUSSIAN PROCESSES, THE PROBLEM OF MAJORIZING OPERATORS)

Abstract

A criterion is given for a Hankel operator , where is the orthogonal projection of onto ) to belong to the Schatten-von Neumann class in terms of its symbol . Various applications are considered: a precise description is obtained for classes of functions definable in terms of rational approximation in the (bounded mean oscillation) norm; it is proved that the averaging projection onto the set of Hankel operators is bounded in the norm of , ; a counterexample is given to a conjecture of Simon on the majorization property in ; a problem of Ibragimov and Solev on stationary Gaussian processes is solved; and a criterion is obtained for functions of an operator in the Sz.-Nagy-Foia? model to belong to the class .Bibliography: 47 titles.