Results 1 to 10 of about 160 (57)

H∞ interpolation constrained by Beurling–Sobolev norms

Moroccan Journal of Pure and Applied Analysis, 2023
We consider a Nevanlinna–Pick interpolation problem on finite sequences of the unit disc, constrained by Beurling–Sobolev norms. We find sharp asymptotics of the corresponding interpolation quantities, thereby improving the known estimates. On our way we
Baranov Anton, Zarouf Rachid
doaj   +1 more source

On the singular factor of a linear combination of holomorphic functions [PDF]

, 2012
We prove that the linear combinations of functions $f_0,...,f_n$ in $H^\infty$ have "few" singular inner factors, provided that the $f_j$'s are suitably smooth up to the boundary, while in general this is no longer true.Comment: 4 ...
Dyakonov, Konstantin M.
core   +3 more sources

On zero sets in the Dirichlet space [PDF]

, 2011
We study the zeros sets of functions in the Dirichlet space. Using Carleson formula for Dirichlet integral, we obtain some new families of zero sets.
A. Nagel, G.T. Cargo, H.S. Shapiro, J. Mashreghi, J. Mashreghi, J. Mashreghi, J. Pau, J.A. Cima, J.G. Caughran, Javad Mashreghi, K. Bogdan, Karim Kellay, L. Carleson, L. Carleson, L. Carleson, L. Carleson, O. El-Fallah, O. El-Fallah, O. Frostman, S. Richter   +19 more
core   +4 more sources

Asymptotic estimates for interpolation and constrained approximation in H2 by diagonalization of Toeplitz operators [PDF]

, 2003
Sharp convergence rates are provided for interpolation and approximation schemes in the Hardy space H-2 that use band-limited data. By means of new explicit formulae for the spectral decomposition of certain Toeplitz operators, sharp estimates for ...
Baratchart, L., Grimm, J., LeBlond, J., Partington, J.R.   +3 more
core   +1 more source

Multiple sampling and interpolation in the classical Fock space

, 2015
We study multiple sampling, interpolation and uniqueness for the classical Fock space in the case of unbounded mul ...
Borichev, Alexander, Hartmann, Andreas, Kellay, Karim, Massaneda, Xavier   +3 more
core   +2 more sources

A reverse Schwarz--Pick inequality

, 2013
We prove a kind of "reverse Schwarz--Pick lemma" for holomorphic self-maps of the disk. The result becomes especially clear-cut for inner functions and casts new light on their derivatives.Comment: 8 pages; to appear in Comput.
Dyakonov, Konstantin M.
core   +1 more source

Similarity of Operators in the Bergman Space Setting

, 2012
We give a necessary and sufficient condition for an n-hypercontraction to be similar to the backward shift operator in a weighted Bergman space. This characterization serves as a generalization of the description given in the Hardy space setting, where ...
Douglas, Ronald G., Kwon, Hyun-Kyoung, Treil, Sergei   +2 more
core   +1 more source

Compact composition operators on Bergman-Orlicz spaces [PDF]

, 2010
We construct an analytic self-map $\phi$ of the unit disk and an Orlicz function $\Psi$ for which the composition operator of symbol $\phi$ is compact on the Hardy-Orlicz space $H^\Psi$, but not compact on the Bergman-Orlicz space ${\mathfrak B}^\Psi ...
Lefèvre, Pascal, Li, Daniel, Queffélec, Hervé, Rodriguez-Piazza, Luis   +3 more
core   +3 more sources

ABC-type estimates via Garsia-type norms

, 2012
We are concerned with extensions of the Mason--Stothers $abc$ theorem from polynomials to analytic functions on the unit disk $\mathbb D$. The new feature is that the number of zeros of a function $f$ in $\mathbb D$ gets replaced by the norm of the ...
Dyakonov, Konstantin M.
core   +1 more source

Boundary behavior of functions in the de Branges--Rovnyak spaces

, 2008
This paper deals with the boundary behavior of functions in the de Branges--Rovnyak spaces. First, we give a criterion for the existence of radial limits for the derivatives of functions in the de Branges--Rovnyak spaces.
Fricain, Emmanuel, Mashreghi, Javad
core   +3 more sources