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

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24 papers · 1 filter

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.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.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.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.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.CV2013★ 8 cited

A reverse Schwarz--Pick inequality

Konstantin M. Dyakonov

We prove a kind of "reverse Schwarz--Pick lemma" for holomorphic self-maps of the disk. The result becomes especially clear-cut for inner functions and casts new light on their der…

math.CV2012

Wronskians and deep zeros of holomorphic functions

Konstantin M. Dyakonov

Given linearly independent holomorphic functions $f_{0}, ..., f_{n}$ on a planar domain $Ω$ , let $E$ be the set of those points $z \in Ω$ where a nontrivial linear combination $\s…

math.CV2012★ 2 cited

On the singular factor of a linear combination of holomorphic functions

Konstantin M. Dyakonov

We prove that the linear combinations of functions $f_{0}, ..., f_{n}$ in $H^{\infty}$ have "few" singular inner factors, provided that the $f_{j}$ 's are suitably smooth up to the boundary,…

math.CV2012★ 1 cited

ABC-type estimates via Garsia-type norms

Konstantin M. Dyakonov

We are concerned with extensions of the Mason--Stothers $ab c$ theorem from polynomials to analytic functions on the unit disk $D$ . The new feature is that the number of zer…

math.CV2011★ 9 cited

Zeros of analytic functions, with or without multiplicities

Konstantin M. Dyakonov

The classical Mason-Stothers theorem deals with nontrivial polynomial solutions to the equation $a + b = c$ . It provides a lower bound on the number of distinct zeros of the polynomial…

math.CV2011★ 3 cited

Factoring derivatives of functions in the Nevanlinna and Smirnov classes

Konstantin M. Dyakonov

We prove that, given a function $f$ in the Nevanlinna class $N$ and a positive integer $n$ , there exist $g \in N$ and $h \in B M O A$ such that $f^{(n)} = g h^{(n)}$ . We may choose $g$ to…

math.CV2010★ 1 cited

Local ABC theorems for analytic functions

Konstantin M. Dyakonov

The classical $ab c$ theorem for polynomials (often called Mason's theorem) deals with nontrivial polynomial solutions to the equation $a + b = c$ . It provides a lower bound for the num…

math.CV2010

Blaschke products and nonideal ideals in higher order Lipschitz algebras

Konstantin M. Dyakonov

We investigate certain ideals (associated with Blaschke products) of the analytic Lipschitz algebra $A^{α}$ , with $α > 1$ , that fail to be "ideal spaces". The latter means that the ide…

math.CV2009★ 2 cited

The Feichtinger conjecture for reproducing kernels in model subspaces

Anton Baranov, Konstantin Dyakonov

We obtain two results concerning the Feichtinger conjecture for systems of normalized reproducing kernels in the model subspace $K_{Θ} = H^{2} ⊖ Θ H^{2}$ of the Hardy space $H^{2}$ , whe…

Carleson-type embeddings with closed range

Extremal problems in BMO and VMO involving the Garsia norm

Interpolation and duality in spaces of pseudocontinuable functions

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

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

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

A reverse Schwarz--Pick inequality

Wronskians and deep zeros of holomorphic functions

On the singular factor of a linear combination of holomorphic functions

ABC-type estimates via Garsia-type norms

Zeros of analytic functions, with or without multiplicities

Factoring derivatives of functions in the Nevanlinna and Smirnov classes

Local ABC theorems for analytic functions

Blaschke products and nonideal ideals in higher order Lipschitz algebras

The Feichtinger conjecture for reproducing kernels in model subspaces

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

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

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