Seminars: V. V. Kapustin, The Hilbert transform with respect to a singular measure

SEMINARS


Seminar on Complex Analysis (Gonchar Seminar) May 26, 2014 18:00, Moscow, Steklov Mathematical Institute, Room 411 (8 Gubkina)

The Hilbert transform with respect to a singular measure V. V. Kapustin St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences
Abstract: A natural definition is introduced for the Hilbert transform on an $L^2$-space with respect to a singular measure on the real line. It is defined as a limit of certain Cauchy-type integrals. Some properties of the class of functions to which the Hilbert transform can be applied are established. The construction is closely connected with averaged wave operators on the singular spectrum.