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pro vyhledávání: '"Dyakonov, Konstantin M."'
Autor:
Dyakonov, Konstantin M.
Publikováno v:
Comptes Rendus. Mathématique, Vol 359, Iss 7, Pp 797-803 (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 $H^1$. We extend this result to subspaces of $H^1$ formed by functions with smaller spectra. More precisely, given a finite se
Externí odkaz:
https://doaj.org/article/75db9aee87834be584cf42642f9e6089
Autor:
Dyakonov, Konstantin M.
Given an $L^2$ function $f$ on the unit circle $\mathbb T$, we put $$\Phi_f(z):=\mathcal P(|f|^2)(z)-|\mathcal Pf(z)|^2,\qquad z\in\mathbb D,$$ where $\mathbb D$ is the open unit disk and $\mathcal P$ is the Poisson integral operator. The Garsia norm
Externí odkaz:
http://arxiv.org/abs/2404.05565
Autor:
Dyakonov, Konstantin M.
Given a Banach space $\mathcal X$, let $x$ be a point in $\text{ball}(\mathcal X)$, the closed unit ball of $\mathcal X$. One says that $x$ is a strongly extreme point of $\text{ball}(\mathcal X)$ if it has the following property: for every $\varepsi
Externí odkaz:
http://arxiv.org/abs/2301.11162
Autor:
Dyakonov, Konstantin M.
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 functions with prescribed spectral gaps. A similar issue is considered for
Externí odkaz:
http://arxiv.org/abs/2211.00853
Autor:
Dyakonov, Konstantin M.
Publikováno v:
Math. Z. 302 (2022), no. 3, 1477--1488
Given an inner function $\theta$ on the unit disk, let $K^p_\theta:=H^p\cap\theta\bar z\bar{H^p}$ be the associated star-invariant subspace of the Hardy space $H^p$. Also, we put $K_{*\theta}:=K^2_\theta\cap{\rm BMO}$. Assuming that $B=B_{\mathcal Z}
Externí odkaz:
http://arxiv.org/abs/2205.12500
Autor:
Dyakonov, Konstantin M.
Publikováno v:
C. R. Math. Acad. Sci. Paris 359 (2021), 797--803
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 $H^1$ formed by functions with smaller spectra. More precisely, given a finite se
Externí odkaz:
http://arxiv.org/abs/2203.09069
Autor:
Dyakonov, Konstantin M.
Given a subset $\Lambda$ of $\mathbb Z_+:=\{0,1,2,\dots\}$, let $H^\infty(\Lambda)$ denote the space of bounded analytic functions $f$ on the unit disk whose coefficients $\widehat f(k)$ vanish for $k\notin\Lambda$. Assuming that either $\Lambda$ or
Externí odkaz:
http://arxiv.org/abs/2110.06713
Autor:
Dyakonov, Konstantin M.
Publikováno v:
Advances in Mathematics 401 (2022), 108330, 22 pp
The Hardy space $H^1$ consists of the integrable functions $f$ on the unit circle whose Fourier coefficients $\widehat f(k)$ vanish for $k<0$. We are concerned with $H^1$ functions that have some additional (finitely many) holes in the spectrum, so w
Externí odkaz:
http://arxiv.org/abs/2102.05857
Autor:
Dyakonov, Konstantin M.
Publikováno v:
Adv. Math. 381 (2021), 107607, 24 pp
Let $\Lambda$ be a finite set of nonnegative integers, and let $\mathcal P(\Lambda)$ be the linear hull of the monomials $z^k$ with $k\in\Lambda$, viewed as a subspace of $L^1$ on the unit circle. We characterize the extreme and exposed points of the
Externí odkaz:
http://arxiv.org/abs/2005.08885
Autor:
Dyakonov, Konstantin M.
Publikováno v:
J. Funct. Anal. 279 (2020), no. 9, 108724, 19 pp
For an inner function $\theta$ on the unit disk, let $K^p_\theta:=H^p\cap\theta\overline{H^p_0}$ be the associated star-invariant subspace of the Hardy space $H^p$. While the squaring operation $f\mapsto f^2$ maps $H^p$ into $H^{p/2}$, one cannot exp
Externí odkaz:
http://arxiv.org/abs/1909.00496