|
Zapiski Nauchnykh Seminarov POMI, 2015, Volume 434, Pages 68–81
(Mi znsl6142)
|
|
|
|
This article is cited in 2 scientific papers (total in 2 papers)
Blaschke product for a Hilbert space with Schwarz–Pick kernel
I. V. Videnskii St. Petersburg State University, St. Petersburg, Russia
Abstract:
For an analog of a Blaschke product for a Hilbert space with Schwarz–Pick kernel (this is a wider class than the class of Hilbert spaces with Nevanlinna–Pick kernel), it is proved that only finitely many elementary multipliers may have zeros on a fixed compact set. It is proved also that the partial Blaschke products multiplied by an appropriate reproducing kernel converge in the Hilbert space. These abstract theorems are applied to the weighted Hardy spaces in the unit disk and to the Drury–Arveson spaces.
Key words and phrases:
Blaschke product, reproducing kernel, multipliers.
Received: 03.08.2015
Citation:
I. V. Videnskii, “Blaschke product for a Hilbert space with Schwarz–Pick kernel”, Investigations on linear operators and function theory. Part 43, Zap. Nauchn. Sem. POMI, 434, POMI, St. Petersburg, 2015, 68–81; J. Math. Sci. (N. Y.), 215:5 (2016), 585–594
Linking options:
https://www.mathnet.ru/eng/znsl6142 https://www.mathnet.ru/eng/znsl/v434/p68
|
Statistics & downloads: |
Abstract page: | 185 | Full-text PDF : | 70 | References: | 38 |
|