SMOOTH FUNCTIONS IN STAR-INVARIANT SUBSPACES

@inproceedings{Khavinson2005SMOOTHFI,
  title={SMOOTH FUNCTIONS IN STAR-INVARIANT SUBSPACES},
  author={Dmitry Khavinson},
  year={2005}
}
In this note we summarize some necessary and sufficient conditions for subspaces invariant with respect to the backward shift to contain smooth functions. We also discuss smoothness of moduli of functions in such subspaces. 
Univalent functions in model spaces: revisited
Motivated by a problem in approximation theory, we find a necessary and sufficient condition for a model (backward shift invariant) subspace $K_\varTheta = H^2\ominus \varTheta H^2$ of the Hardy
Model Spaces: a Survey
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
Recent Progress on Truncated Toeplitz Operators
This paper is a survey on the emerging theory of truncated Toeplitz operators. We begin with a brief introduction to the subject and then highlight the many recent developments in the field since
On model spaces and density of functions regular on the boundary
We characterize the model spaces KΘ in which functions with smooth boundary extensions are dense. It turns out that such approximation is possible if and only if the singular measure associated to
On model spaces and density of functions smooth on the boundary
We characterize the model spaces KΘ in which functions with smooth boundary extensions are dense. It is shown that such approximations are possible if and only if the singular measure associated to
Construction of some smooth Cauchy transforms
For a given Beurling-Carleson subset E of the unit circle T of has positive Lebesgue measure, we give explicit formulas for measurable functions supported on E such that their Cauchy transforms have
An abstract approach to approximations in spaces of pseudocontinuable functions
We give an abstract approach to approximations with a wide range of regularity classes X in spaces of pseudocontinuable functions K p θ, where θ is an inner function and p > 0. More precisely, we
Cyclic inner functions in growth classes and applications to approximation problems
It is well-known that for any inner function θ defined in the unit disk D the following two conditons: ( i ) there exists a sequence of polynomials { p n } n such that lim n →∞ θ ( z ) p n ( z ) = 1
One phase problem for two positive harmonic function: below the codimension $1$ threshold
. What can be said about the domain Ω in R n for which its Green’s function G ( z ) satisfies G ( z ) (cid:16) dist( z, ∂ Ω) δ ? What can we say about Ω if the Boundary Harnack Principle holds in the
C V ] 1 J un 2 02 1 FREE BOUNDARY PROBLEMS VIA SAKAI
A Schwarz function on an open domain Ω is a holomorphic function satisfying S(ζ) = ζ on Γ, which is part of the boundary of Ω. Sakai in 1991 gave a complete characterization of the boundary of a
...
...

References

SHOWING 1-10 OF 18 REFERENCES
Analytic Functions Smooth up to the Boundary
Notations.- The (F)-property.- Moduli of analytic functions smooth up to the boundary.- Zeros and their multiplicities.- Closed ideals in the space X pq ? (?,?).
Bounded Analytic Functions
Preliminaries.- Hp Spaces.- Conjugate Functions.- Some Extremal Problems.- Some Uniform Algebra.- Bounded Mean Oscillation.- Interpolating Sequences.- The Corona Construction.- Douglas Algebras.-
Inner functions and cyclic vectors in the Bloch space
In this paper we construct a singular inner function whose polynomial multiples are dense in the little Bloch space qo . To do this we construct a singular measure on the unit circle with "best
Zero sets and multiplier theorems for star-invariant sub spaces
Given an inner function θ, let {Kskθ/p}:= Hp ∩θ {Hsk0/p} be the corresponding star-invariant subspace of the Hardy spaceHp. We show that, unless θ is a finite Blaschke product, the zero sets for
The Backward Shift on the Hardy Space
Introduction Classical boundary value results The Hardy spaces of the disk The Hardy spaces of the upper-half plane The backward shift on $H^p$ for $p \in [1,\infty)$ The backward shift on $H^p$ for
Moduli and arguments of analytic functions from subspaces of Hp that are invariant for the backward shift operator
= K~{c+)d~---etHP(C+)NOH~(C+), I ~p ~+oo (Now, 8 and elements of classes HP are functions defined almost everywhere on the line R=FrC+). Endowed with the LP-norm, KOP becomes a Banach space for 1 0
The Bergman Spaces
In this chapter we introduce the Bergman spaces and concentrate on the general aspects of these spaces. Most results are concerned with the Banach (or metric) space structure of Bergman spaces.
Ideals in Rings of Analytic Functions with Smooth Boundary Values
Let A denote the Banach algebra of functions analytic in the open unit disc D and continuous in . If f and its first m derivatives belong to A, then the boundary function f(eiθ) belongs to Cm(∂D).
Equivalent norms on lipschitz-type spaces of holomorphic functions
A continuous function w: [0, +ce)--~R with w(0)=0 will be called a majorant if ~(t) is increasing and w(t)/t is nonincreasing for t>0. If, in addition, there is a constant C(w)>0 such that Je t2 dt
...
...