Zobrazeno 1 - 10
of 113
pro vyhledávání: '"Lykova, Zinaida"'
Publikováno v:
J. Math. Anal. Appl. (2024), 128732
Let $E$ be the open region in the complex plane bounded by an ellipse. The B. and F. Delyon norm $\|\cdot\|_{\mathrm{bfd}}$ on the space $\mathrm{Hol}(E)$ of holomorphic functions on $E$ is defined by $$ \|f\|_{\mathrm{bfd}} \stackrel{\rm def}{=} \su
Externí odkaz:
http://arxiv.org/abs/2407.03156
We give new necessary and sufficient conditions for the numerical range $W(T)$ of an operator $T \in \mathcal{B}(\mathcal{H})$ to be a subset of the closed elliptical set $K_\delta \subseteq \mathbb{C}$ given by \[ K_\delta {\stackrel{\rm def}{=}} \l
Externí odkaz:
http://arxiv.org/abs/2311.00680
In this paper we prove a Schwarz lemma for the pentablock. The set \[ \mathcal{P}=\{(a_{21}, \text{tr} \ A, \det A) : A=[a_{ij}]_{i,j=1}^2 \in \mathbb{B}^{2\times 2}\} \] where $\mathbb{B}^{2\times 2}$ denotes the open unit ball in the space of $2\ti
Externí odkaz:
http://arxiv.org/abs/2205.07306
We introduce the notion of a pseudomultiplier of a Hilbert space $\mathcal H$ of functions on a set $\Omega$. Roughly, a pseudomultiplier of $\mathcal H$ is a function which multiplies a finite-codimensional subspace of $\mathcal H$ into $\mathcal H$
Externí odkaz:
http://arxiv.org/abs/2205.05012
Publikováno v:
In Journal of Functional Analysis 15 October 2024 287(8)
Publikováno v:
In Journal of Mathematical Analysis and Applications 15 January 2025 541(2)
We survey the Carath\'eodory extremal problem $\mathrm{Car} \delta$ on the symmetrized bidisc $$ G = \{(z+w,zw):|z|<1, \, |w|<1\} = \{(s,p)\in \mathbb{C}^2: |s-\bar s p| < 1-|p|^2\}. $$ We also give some new results on this topic. We are particularly
Externí odkaz:
http://arxiv.org/abs/2201.09078
The set \[ \overline{\mathbb{E}}= \{ x \in {\mathbb{C}}^3: \quad 1-x_1 z - x_2 w + x_3 zw \neq 0 \mbox{ whenever } |z| < 1, |w| < 1 \} \] is called the tetrablock and has intriguing complex-geometric properties. It is polynomially convex, nonconvex a
Externí odkaz:
http://arxiv.org/abs/2101.02739
The tetrablock is the set $$ \mathcal{E}=\{x \in \mathbb{C}^3: \quad 1-x_1z-x_2w+x_3z w \neq 0 \quad whenever \quad |z|\leq 1, |w|\leq 1\}. $$ The closure of $\mathcal{E}$ is denoted by $\overline{\mathcal{E}}$. A tetra-inner function is an analytic
Externí odkaz:
http://arxiv.org/abs/2101.02306
The symmetrized bidisc \[ G \stackrel{\rm{def}}{=}\{(z+w,zw):|z|<1,\ |w|<1\}, \] under the Carath\'eodory metric, is a complex Finsler space of cohomogeneity $1$ in which the geodesics, both real and complex, enjoy a rich geometry. As a Finsler manif
Externí odkaz:
http://arxiv.org/abs/2012.03304