# An abstract approach to approximations in spaces of pseudocontinuable functions

@inproceedings{Limani2021AnAA,
title={An abstract approach to approximations in spaces of pseudocontinuable functions},
year={2021}
}
• Published 17 June 2021
• Mathematics
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 demonstrate a general principle, attributed to A. B. Aleksandrov, which asserts that if a certain linear manifold X is dense in the space of pseudocontinuable functions K p0 θ , for some p0 > 0, then X is in fact dense in K p θ, for all p > 0. Moreover, for a rich class of Banach spaces of analytic…
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## References

SHOWING 1-10 OF 21 REFERENCES

### On bounded analytic functions

The objective of this paper is to give an alternative derivation of results on bounded analytic functions recently obtained by Ahlfors [1] and Garabedian [2].1 While it is admitted that the main idea

### On model spaces and density of functions regular on the boundary

• Mathematics
• 2021
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 the existence of nontangential boundary values of pseudocontinuable functions

AbstractLet θ be an inner function, let θ*(H2)=H2⊖θH2, and let μ be a finite Borel measure on the unit circle $$\mathbb{T}$$ . Our main purpose is to prove that, if every functionf∈θ*(H2) can be

### Division and Multiplication by Inner Functions and Embedding Theorems for Star-Invariant Subspaces

In this paper the full answer is obtained for the following classes X: the space BMO of functions of bounded mean oscillation, the algebra QC of quasidef continuous functions, the space 9= mult(BMO)

### Cyclic elements in some spaces of analytic functions

DEFINITIONS. 1. A~ (p > 0) is the Banach space of analytic functions f(z) in U = {z G C| \z\ < 1} that satisfy \f(z)\ = o[(l \z\)~] (\z\ > 1) with the norm \\f\\ = max{ |f(z)\(l z)} (z G If). Note

### On cyclic vectors of the backward shift

• Mathematics
• 1967
The forward shift operator U ( that is, multiplication by the independent variable) on the space H of the unit circle has been much studied. In particular it is known that a vector ƒ is cyclic (that

### Linear Operators

Linear AnalysisMeasure and Integral, Banach and Hilbert Space, Linear Integral Equations. By Prof. Adriaan Cornelis Zaanen. (Bibliotheca Mathematica: a Series of Monographs on Pure and Applied

### The Backward Shift on the Hardy Space

• Mathematics
• 2000
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