Continual sets with the Dirichlet properties and products of Hardy spaces
Abstract
The problem on the simultaneous approximation of functions from the Hardy spaces by continuous functions on the Riemann sphere for a system of disjoint simply connected domains is considered. A criterion for the solvability of this problem is established.
References
Gamelin T.W., Garnett J.В Pointwise bounded approximation and Dirichlet algebras // J. Fund. Anal.– 1971.–8.–P.360–404.
Duren P.L. Theory of $H^p$ spaces.–New York; London: Acad. press, 1970.–258 p.
Glicksberg I. Dominant representing measures and rational approximation // Trans. Amer. Math. Soc. – 1968.– 130.– P.425–462.
Browder A., Wermer J. Some algebras of function on an arc //J. Math. and Mech.–1963.–12.–P.119–130.
Davie A.M. Dirichlet algebras of analytic functions //J. Fund. Anal.–1970. – 6. – P.348–356.
Davie A.M. Bounded approximation and Dirichlet sets // Ibid – P.460–467.
Иосида К. Функциональный анализ. –М.: Мир. 1967.– 625с.
Довгошей А.А. Приближение аналитических функций в некоторых функциональных пространствах и рациональная аппроксимация функций из классов Харди // Докл. АН УССР. Сер.А. – 1990.– №10.– С. 19–21.
Довгошей А.А. Об интегральных представлениях в классах Харди и наилучших приближениях в некоторых функциональных пространствах//Укр. маг. журн. – 1991 – 43, №3. –С. 342–347.
Bishop C.J., Carleson L., Garnett J.В., Jones P.W. Harmonic measures supported on curves //Pacif. J. Math. – 1989. – 138. – P. 233–236.
Bishop C.J. Constructing continuous functions holomorphic off a curve // J. Fund. Anal. – 1989. –82.–P. 113–137.
Copyright (c) 1992 A. A. Dovgoshey
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