# Functions with small and large spectra as (non)extreme points in subspaces of $H^\infty$

@inproceedings{Dyakonov2021FunctionsWS, title={Functions with small and large spectra as (non)extreme points in subspaces of \$H^\infty\$}, author={Konstantin M. Dyakonov}, year={2021} }

Given a subset Λ of Z+ := {0, 1, 2, . . .}, let H ∞(Λ) denote the space of bounded analytic functions f on the unit disk whose coefficients f̂(k) vanish for k / ∈ Λ. Assuming that either Λ or Z+ \ Λ is finite, we determine the extreme points of the unit ball in H∞(Λ).

## References

SHOWING 1-10 OF 15 REFERENCES

Nearly outer functions as extreme points in punctured Hardy spaces

- Mathematics
- 2021

The Hardy space H consists of the integrable functions f on the unit circle whose Fourier coefficients f̂(k) vanish for k < 0. We are concerned with H functions that have some additional (finitely…

Extreme points in spaces of polynomials

- Mathematics
- 2003

We determine the extreme points of the unit ball in spaces of complex polynomials (of a fixed degree), living either on the unit circle or on a subset of the real line and endowed with the supremum…

ON INTERPOLATING FUNCTIONS WITH MINIMAL NORM

- Mathematics
- 1978

Let Hx denote the Banach algebra of bounded analytic functions in the unit disc (z: \z\ 1 if h e H°° and h # 0. An application of this result to the theory of best approximation is given.

Banach spaces of analytic functions

- Mathematics
- 1996

In this paper, we explore certain Banach spaces of analytic functions. In particular, we study the space A -I, demonstrating some of its basic properties including non-separability. We ask the…

Polynomials and entire functions: zeros and geometry of the unit ball

- Mathematics
- 2000

We characterize the extreme and exposed points of the unit ball in certain L 1 -spaces of polynomials and entire functions. As usual, an element x ∈ b (X) is said to be an extreme point of b(X )i f…

Two Problems on Coinvariant Subspaces of the Shift Operator

- Mathematics
- 2014

Two problems are posed that involve the star-invariant subspace $${K^{p}_{\theta}}$$Kθp (in the Hardy space Hp) associated with an inner function $${\theta}$$θ. One of these asks for a…

INTERPOLATING FUNCTIONS OF MINIMAL NORM, STAR-INVARIANT SUBSPACES, AND KERNELS OF TOEPLITZ OPERATORS

- Mathematics
- 1992

It is proved that for each inner function 6 there exists an inter- polating sequence {zn} in the disk such that sup" |o(z")| 1 . Some results are obtained concerning interpolation in the…

A Rudin–de Leeuw type theorem for functions with spectral gaps

- Comptes Rendus. Mathématique
- 2021

Our starting point is a theorem of de Leeuw and Rudin that describes the extreme points of the unit ball in the Hardy space H1. We extend this result to subspaces of H1 formed by functions with…

On bounded analytic functions

- Mathematics
- 1950

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…

The maximum modulus of a trigonometric trinomial

- Mathematics
- 2008

Let Γ be a set of three integers and let be the space of 2π-periodic functions with spectrum in Γ endowed with the maximum modulus norm. We isolate the maximum modulus points x of trigonometric…