Free interpolation of germs of analytic functions in Hardy spaces
- 21 Downloads
One proves theorems on the interpolation of germs of analytic functions, defined in the neighborhoods of the interpolation nodes, in the Hardy spaces HP(0 < p ⩽ +∞), generalizing the corresponding results of N. K. Nikol'skii and V. I. Vasyunin for the classes H∞ and H2. One obtains estimates of the norms of the interpolating functions in terms of the parameter of the set on which the interpolation is performed.
KeywordsAnalytic Function Hardy Space Interpolation Node Free Interpolation
Unable to display preview. Download preview PDF.
- 1.N. K. Nikol'skii, “Bases of invariant subspaces and operator interpolation,” Tr. Mat. Inst. Akad. Nauk SSSR,130, 50–123 (1978).Google Scholar
- 2.N. K. Nikol'skii, Lectures on the Shift Operator [in Russian], Nauka, Moscow (1980).Google Scholar
- 3.V. I. Vasyunin, “Unconditionally convergent spectral decompositions and interpolation problems,” Tr. Mat. Inst. Akad. Nauk SSSR,130, 5–49 (1978).Google Scholar
- 4.L. Carleson, “Interpolations by bounded analytic functions and the corona problem,” Ann. Math.,76, No. 3, 547–559 (1962).Google Scholar
- 5.W. Rudin, Functional Analysis, McGraw-Hill, New York (1973).Google Scholar
- 6.V. M. Martirosyan, “The effective solution of multiple interpolation problems in H∞ by the application of M. M. Dzhrbashyan's biorthogonalization method,” Preprint Inst. Mat. Akad. Nauk ArmSSR (1981).Google Scholar
- 7.S.A. Vinogradov, “Some remarks on the free interpolation by bounded and slowly increasing analytic functions,” J. Sov. Math.,27, No. 1 (1984).Google Scholar
- 8.G. M. Airapetyan, “Multiple interpolation and the basis property of certain biorthogonal systems of rational functions in the Hardy HP classes,” Izv. AN ArmSSR, Ser. Mat.,12, No. 4, 262–277 (1977).Google Scholar
- 9.M. M. Dzhrbashyan, “The basis property of certain biorthogonal systems, and the solution of a multiple interpolation problem in HP classes in the half plane,” Izv. Akad. Nauk SSSR, Ser. Mat.,43, No. 6, 1322–1384 (1978).Google Scholar