14 citations · 103 across the 31 of their papers we have counts for
8 papers · 1 filter
The strong reproducing kernel thesis for Hankel operators and the Garsia norm
Konstantin M. Dyakonov
Given a reproducing kernel Hilbert space and a bounded operator on , we say that obeys the strong reproducing kernel thesis (SRKT) if $\|T\|=\sup_k…
Extreme points in quotients of Hardy spaces
Konstantin M. Dyakonov
In the Hardy spaces and , there are neat and well-known characterizations of the extreme points of the unit ball. We obtain counterparts of these classical theorems…
Inner functions as strongly extreme points: stability properties
Konstantin M. Dyakonov
Given a Banach space , let be a point in , the closed unit ball of . One says that is a strongly extreme point of $\text{ba…
Questions about extreme points
Konstantin M. Dyakonov
We discuss the geometry of the unit ball -- specifically, the structure of its extreme points (if any) -- in subspaces of and on the circle that are formed by func…
A Rudin--de Leeuw type theorem for functions with spectral gaps
Konstantin M. Dyakonov
Our starting point is a theorem of de Leeuw and Rudin that describes the extreme points of the unit ball in the Hardy space . We extend this result to subspaces of forme…
Nearly outer functions as extreme points in punctured Hardy spaces
Konstantin M. Dyakonov
The Hardy space consists of the integrable functions on the unit circle whose Fourier coefficients vanish for . We are concerned with functions…
Lacunary polynomials in : geometry of the unit sphere
Konstantin M. Dyakonov
Let be a finite set of nonnegative integers, and let be the linear hull of the monomials with , viewed as a subspace of on the unit circle. W…
Two problems on coinvariant subspaces of the shift operator
Konstantin M. Dyakonov
Two problems are posed that involve the star-invariant subspace (in the Hardy space ) associated with an inner function . One of these asks for a characterization o…