Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userInterpolation in Model Spaces
240
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
In this paper we consider interpolation in model spaces, $H^2 ominus B H^2$ with $B$ a Blaschke product. We study unions of interpolating sequences for two sequences that are far from each other in the pseudohyperbolic metric as well as two sequences that are close to each other in the pseudohyperbolic metric. The paper concludes with a discussion of the behavior of Frostman sequences under perturbations.
rate research
Read More
Most characterizations of interpolating sequences for Bergman spaces include the condition that the sequence be uniformly discrete in the hyperbolic metric. We show that if the notion of interpolation is suitably generalized, two of these characterizations remain valid without that condition. The general interpolation we consider here includes the usual simple interpolation and multiple interpolation as special cases.
We extend our work on nonseparated interpolating sequences, originally developed for Bergman spaces with weights of the form $(1 - |z|^2)^alpha$, to more general weights.
This paper extends the known characterization of interpolation and sampling sequences for Bergman spaces to the mixed-norm spaces. The Bergman spaces have conformal invariance properties not shared by the mixed-norm spaces. As a result, different techniques of proof were required.
In this paper we examine the multipliers from one model space to another.
The Patterson-Sullivan construction is proved almost surely to recover a Bergman function from its values on a random discrete subset sampled with the determinantal point process induced by the Bergman kernel on the unit ball $mathbb{D}_d$ in $mathbb{C}^d$. For super-critical weighted Bergman spaces, the interpolation is uniform when the functions range over the unit ball of the weighted Bergman space. As main results, we obtain a necessary and sufficient condition for interpolation of a fixed pluriharmonic function in the complex hyperbolic space of arbitrary dimension (cf. Theorem 1.4 and Theorem 4.11); optimal simultaneous uniform interpolation for weighted Bergman spaces (cf. Theorem 1.8, Proposition 1.9 and Theorem 4.13); strong simultaneous uniform interpolation for weighted harmonic Hardy spaces (cf. Theorem 1.11 and Theorem 4.15); and establish the impossibility of the uniform simultaneous interpolation for the Bergman space $A^2(mathbb{D}_d)$ on $mathbb{D}_d$ (cf. Theorem 1.12 and Theorem 6.7).
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
