TY - JOUR

T1 - Blaschke product for a Hilbert space with Schwarz-Pick kernel

AU - Videnskii, I. V.

N1 - Videnskii, I.V. Blaschke Product for a Hilbert Space with Schwarz–Pick Kernel. J Math Sci 215, 585–594 (2016). https://doi.org/10.1007/s10958-016-2864-4

PY - 2016/6

Y1 - 2016/6

N2 - or 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 also proved that 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.

AB - or 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 also proved that 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.

KW - Hilbert space

KW - Unit Disk

KW - Hardy spaces

KW - Bergman space

KW - Blaschke product

UR - https://link.springer.com/article/10.1007/s10958-016-2864-4

M3 - Article

VL - 215

SP - 585

EP - 594

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -