Konstantin M. Dyakonov

activity

20092026

most citedUnivalent polynomials and Koebe's one-quarter theorem

14 citations · 103 across the 31 of their papers we have counts for

collaborators

33 papers

math.FA2026

The strong reproducing kernel thesis for Hankel operators and the Garsia norm

Konstantin M. Dyakonov

Given a reproducing kernel Hilbert space $H$ and a bounded operator $T$ on $H$ , we say that $T$ obeys the strong reproducing kernel thesis (SRKT) if $\|T\|=\sup_k…

math.FA2026

Extreme points in quotients of Hardy spaces

Konstantin M. Dyakonov

In the Hardy spaces $H^{1}$ and $H^{\infty}$ , there are neat and well-known characterizations of the extreme points of the unit ball. We obtain counterparts of these classical theorems…

math.CV2025

Carleson-type embeddings with closed range

Konstantin M. Dyakonov

We characterize the Carleson measures $μ$ on the unit disk for which the image of the Hardy space $H^{p}$ under the corresponding embedding operator is closed in $L^{p} (μ)$ . In fact, a…

math.CV2024

Extremal problems in BMO and VMO involving the Garsia norm

Konstantin M. Dyakonov

Given an $L^{2}$ function $f$ on the unit circle $T$ , we put $Φ_{f} (z) := P (∣ f ∣^{2}) (z) - ∣ P f (z) ∣^{2}, z \in D,$ where $D$ is the open unit disk…

math.FA2023★ 2 cited

Inner functions as strongly extreme points: stability properties

Konstantin M. Dyakonov

Given a Banach space $X$ , let $x$ be a point in $ball (X)$ , the closed unit ball of $X$ . One says that $x$ is a strongly extreme point of $\text{ba…

math.FA2022

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 $L^{1}$ and $L^{\infty}$ on the circle that are formed by func…

math.CV2022★ 1 cited

Interpolation and duality in spaces of pseudocontinuable functions

Konstantin M. Dyakonov

Given an inner function $θ$ on the unit disk, let $K_{θ}^{p} := H^{p} \cap θ z ˉ H^{p} ˉ$ be the associated star-invariant subspace of the Hardy space $H^{p}$ . Also, we put $K_{*θ}:=K^2_θ\c…

math.FA2022★ 5 cited

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 $H^{1}$ . We extend this result to subspaces of $H^{1}$ forme…

math.CV2021

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

Konstantin M. Dyakonov

Given a subset $Λ$ of $Z_{+} := {0, 1, 2, \dots}$ , let $H^{\infty} (Λ)$ denote the space of bounded analytic functions $f$ on the unit disk whose coefficients $f (k)$ vanis…

math.FA2021★ 9 cited

Nearly outer functions as extreme points in punctured Hardy spaces

Konstantin M. Dyakonov

The Hardy space $H^{1}$ consists of the integrable functions $f$ on the unit circle whose Fourier coefficients $f (k)$ vanish for $k < 0$ . We are concerned with $H^{1}$ functions…

math.FA2020★ 9 cited

Lacunary polynomials in $L^{1}$ : geometry of the unit sphere

Konstantin M. Dyakonov

Let $Λ$ be a finite set of nonnegative integers, and let $P (Λ)$ be the linear hull of the monomials $z^{k}$ with $k \in Λ$ , viewed as a subspace of $L^{1}$ on the unit circle. W…

math.CV2019

Quasi-squares of pseudocontinuable functions

Konstantin M. Dyakonov

For an inner function $θ$ on the unit disk, let $K_{θ}^{p} := H^{p} \cap θ H_{0}^{p}$ be the associated star-invariant subspace of the Hardy space $H^{p}$ . While the squaring operation $…

math.CV2018★ 14 cited

Univalent polynomials and Koebe's one-quarter theorem

Dmitriy Dmitrishin, Konstantin Dyakonov, Alex Stokolos

The famous Koebe $\frac{1}{4}$ theorem deals with univalent (i.e., injective) analytic functions $f$ on the unit disk $D$ . It states that if $f$ is normalized so that $f (0) = 0$ …

math.CV2018★ 3 cited

An extremal problem for functions annihilated by a Toeplitz operator

Konstantin M. Dyakonov

For a bounded function $φ$ on the unit circle $T$ , let $T_{φ}$ be the associated Toeplitz operator on the Hardy space $H^{2}$ . Assume that the kernel $$K_2(φ):=\{f\in H^2:\,T_φ…

math.CV2018★ 2 cited

Interpolating by functions from model subspaces in $H^{1}$

Konstantin M. Dyakonov

Given an interpolating Blaschke product $B$ with zeros ${a_{j}}$ , we seek to characterize the sequences of values ${w_{j}}$ for which the interpolation problem $$f(a_j)=w_j\qquad (…

math.CV2017★ 5 cited

A free interpolation problem for a subspace of $H^{\infty}$

Konstantin M. Dyakonov

Given an inner function $θ$ , the associated star-invariant subspace $K_{θ}^{\infty}$ is formed by the functions $f \in H^{\infty}$ that annihilate (with respect to the usual pairing) the…

math.CV2017★ 3 cited

Factorization and non-factorization theorems for pseudocontinuable functions

Konstantin M. Dyakonov

Let $θ$ be an inner function on the unit disk, and let $K_{θ}^{p} := H^{p} \cap θ H_{0}^{p}$ be the associated star-invariant subspace of the Hardy space $H^{p}$ , with $p \geq 1$ . While a n…

math.HO2017

Remembering Victor Petrovich Havin

Konstantin M. Dyakonov

These are reminiscences of V. P. Havin (1933--2015), founder of the modern St. Petersburg analysis school.

math.CV2016★ 2 cited

Smooth analytic functions and model subspaces

Konstantin M. Dyakonov

The main themes of this survey are as follows: (a) the canonical (Riesz--Nevanlinna) factorization in various classes of analytic functions on the disk that are smooth up to its bo…

math.CV2016★ 6 cited

Functions in Bloch-type spaces and their moduli

Konstantin M. Dyakonov

Given a suitably regular nonnegative function $ω$ on $(0, 1]$ , let $B_{ω}$ denote the space of all holomorphic functions $f$ on the unit ball $B_{n}$ of $C^{n}$ t…

math.CV2015★ 5 cited

Inner functions and inner factors of their derivatives

Konstantin M. Dyakonov

For an inner function $θ$ with $θ^{'} \in N$ , where $N$ is the Nevanlinna class, several problems are posed in connection with the canonical (inner-outer) factorizatio…

math.CV2014★ 9 cited

A characterization of Möbius transformations

Konstantin M. Dyakonov

We prove that the derivative $θ^{'}$ of an inner function $θ$ is outer if and only if $θ$ is a Möbius transformation. An alternative characterization involving a reverse Schwarz--Pick…

math.CV2014

Boundary Gauss--Lucas type theorems on the disk

Konstantin M. Dyakonov

The classical Gauss--Lucas theorem describes the location of the critical points of a polynomial. There is also a hyperbolic version, due to Walsh, in which the role of polynomials…

math.FA2014★ 2 cited

Two problems on coinvariant subspaces of the shift operator

Konstantin M. Dyakonov

Two problems are posed that involve the star-invariant subspace $K_{θ}^{p}$ (in the Hardy space $H^{p}$ ) associated with an inner function $θ$ . One of these asks for a characterization o…

The strong reproducing kernel thesis for Hankel operators and the Garsia norm

Extreme points in quotients of Hardy spaces

Carleson-type embeddings with closed range

Extremal problems in BMO and VMO involving the Garsia norm

Inner functions as strongly extreme points: stability properties

Questions about extreme points

Interpolation and duality in spaces of pseudocontinuable functions

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

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

Nearly outer functions as extreme points in punctured Hardy spaces

Lacunary polynomials in L1: geometry of the unit sphere

Quasi-squares of pseudocontinuable functions

Univalent polynomials and Koebe's one-quarter theorem

An extremal problem for functions annihilated by a Toeplitz operator

Interpolating by functions from model subspaces in H1

A free interpolation problem for a subspace of H∞

Factorization and non-factorization theorems for pseudocontinuable functions

Remembering Victor Petrovich Havin

Smooth analytic functions and model subspaces

Functions in Bloch-type spaces and their moduli

Inner functions and inner factors of their derivatives

A characterization of Möbius transformations

Boundary Gauss--Lucas type theorems on the disk

Two problems on coinvariant subspaces of the shift operator

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

Lacunary polynomials in $L^{1}$ : geometry of the unit sphere

Interpolating by functions from model subspaces in $H^{1}$

A free interpolation problem for a subspace of $H^{\infty}$