Advertisement

Multipliers and Divisors of Cauchy—Stieltjes Integrals

  • S. A. Vinogradov
  • M. G. Goluzina
  • V. P. Khavin
Chapter
Part of the Seminars in Mathematics book series (SM)

Abstract

Let U be an open unit circle on the complex plane, let ә U be its boundary, and let z be the complex variable. In the present article we investigate the multiplicative properties of functions g representable in U by an integral of the Cauchy—Stieltjes type:
(1)
in which M is a complex Borel measure on U. We denote the set of all such functions g by K. The set K is linear under the ordinary operations of addition of functions and multiplication of a function by a complex number.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    Privalov, L L, Boundary Properties of Analytic Functions, GITTL (1950).Google Scholar
  2. 2.
    Hoffman, K., Banach Spaces of Analytic Functions [Russian translation], IIL (1963) [English edition: Prentice-Hall, Englewood Cliffs (N. J.) (1962)].Google Scholar
  3. 3.
    Khavin, V. P., On analytic functions representable by Cauchy=Stieltjes integrals, Vestnik Lenin- grad. Univ. (LGU), Ser. Matem. Mekh. Astron., 1 (1): 66–79 (1958).Google Scholar
  4. 4.
    Khavin, V. P., On the relations between certain classes of functions regular in the unit disk, Vestnik Leningrad. Univ. (LGU), Ser. Matem. Mekh. Astron., 1 (1): 102–110 (1962).Google Scholar
  5. 5.
    Landau, E. Darstellung and Begrundung einiger neuerer Ergebnisse der Funktionentheorie, Berlin (1929).Google Scholar

Copyright information

© Springer Science+Business Media New York 1972

Authors and Affiliations

  • S. A. Vinogradov
  • M. G. Goluzina
  • V. P. Khavin

There are no affiliations available

Personalised recommendations