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of 275
pro vyhledávání: '"32A07"'
Autor:
Tomar, Nitin
In this note, we provide an alternative way of describing the distinguished boundariesof symmetrized bidisc, tetrablock and pentablock. We show that each of these distinguished boundaries can be characterized as the union of orbits of two elements un
Externí odkaz:
http://arxiv.org/abs/2403.01159
Autor:
Chen, Liwei, Yuan, Yuan
The Hardy spaces are defined on the quotient domain of a bounded complete Reinhardt domain by a finite subgroup of $U(n)$. The Szeg\H{o} projection on the quotient domain can be studied by lifting to the covering space. This setting builds on the sol
Externí odkaz:
http://arxiv.org/abs/2310.12151
Autor:
Biswas, Anindya, Maitra, Anwoy
Publikováno v:
J. Math. Anal. Appl. 504 (2021), no. 2, Paper No. 125434, 10 pp
We make a connection between the structure of the bidisc and a distinguished subgroup of its automorphism group. The automorphism group of the bidisc, as we know, is of dimension six and acts transitively. We observe that it contains a subgroup that
Externí odkaz:
http://arxiv.org/abs/2104.05001
Autor:
Balakumar, G. P.
It is a classical fact that domains of convergence of power series of several complex variables are characterized as logarithmically convex complete Reinhardt domains; let $D \subsetneq \mathbb{C}^N$ be such a domain. We show that a necessary as well
Externí odkaz:
http://arxiv.org/abs/2103.13986
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
Publikováno v:
Eur. J. Math.8(2022), no.1, 403-416
We obtain $L^p$ estimates for Toeplitz operators on the generalized Hartogs triangles $\mathbb{H}_\gamma = \{(z_1,z_2) \in \mathbb{C}^2: |z_1|^\gamma < |z_2|<1\}$ for two classes of positive radial symbols, one a power of the distance to the origin,
Externí odkaz:
http://arxiv.org/abs/2009.07260
Autor:
Nagel, Alexander, Pramanik, Malabika
For appropriate domains $\Omega_{1}, \Omega_{2}$ we consider mappings $\Phi_{\mathbf A}:\Omega_{1}\to\Omega_{2}$ of monomial type. We obtain an orthogonal decomposition of the Bergman space $\mathcal A^{2}(\Omega_{1})$ into finitely many closed subsp
Externí odkaz:
http://arxiv.org/abs/2002.02915
Publikováno v:
In: Current Trends in Analysis, its Applications and Computation, pp. 357-362. Trends in Mathematics, Birkh\"auser, Cham, 2022
Analytic functions defined on a tube domain $T^{C}\subset \mathbb{C}^{n}$ and taking values in a Banach space $X$ which are known to have $X$-valued distributional boundary values are shown to be in the Hardy space $H^{p}(T^{C},X)$ if the boundary va
Externí odkaz:
http://arxiv.org/abs/2001.10021
Autor:
Monguzzi, Alessandro
The definition of classical holomorphic function spaces such as the Hardy space or the Dirichlet space on the Hartogs triangle is not canonical. In this paper we introduce a natural family of holomorphic function spaces on the Hartogs triangle which
Externí odkaz:
http://arxiv.org/abs/1910.13741