Functions with small and large spectra as (non)extreme points in subspaces of 𝐻^{∞}

Author:

Dyakonov K.

Abstract

Given a subset Λ \Lambda of Z + { 0 , 1 , 2 , } \mathbb Z_+≔\{0,1,2,\dots \} , let H ( Λ ) H^\infty (\Lambda ) denote the space of bounded analytic functions f f on the unit disk whose coefficients f ^ ( k ) \widehat f(k) vanish for k Λ k\notin \Lambda . Assuming that either Λ \Lambda or Z + Λ \mathbb Z_+\setminus \Lambda is finite, we determine the extreme points of the unit ball in H ( Λ ) H^\infty (\Lambda ) .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Algebra and Number Theory,Analysis

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