Results 41 to 50 of about 4,865 (165)
Restriction of Toeplitz Operators on Their Reducing Subspaces
Journal of Function Spaces, Volume 2017, Issue 1, 2017., 2017 We study the restrictions of analytic Toeplitz operator on its minimal reducing subspaces for the unit disc and construct their models on slit domains. Furthermore, it is shown that Tzn is similar to the sum of n copies of the Bergman shift.
Anjian Xu, Yang Zou, Raúl E. Curto
wiley +1 more source
Abstract and Applied Analysis, 2015 Let Ω be a smoothly bounded pseudoconvex domain in Cn with one degenerate eigenvalue and assume that there is a smooth holomorphic curve V whose order of contact with bΩ at z0∈bΩ is larger than or equal to η.
Sanghyun Cho, Young Hwan You
doaj +1 more source
Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.Abstract Using iterated uniform local completion, we introduce a notion of continuous CR$CR$ functions on locally closed subsets of reduced complex spaces, generalising both holomorphic functions and CR$CR$ functions on CR$CR$ submanifolds. Under additional assumptions of set‐theoretical weak pseudo‐concavity, we prove optimal maximum modulus ...
Mauro Nacinovich, Egmont Porten
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Szegö Kernels and Asymptotic Expansions for Legendre Polynomials
Journal of Complex Analysis, Volume 2017, Issue 1, 2017., 2017 We present a geometric approach to the asymptotics of the Legendre polynomials Pk,n+1, based on the Szegö kernel of the Fermat quadric hypersurface, leading to complete asymptotic expansions holding on expanding subintervals of [−1,1].
Roberto Paoletti, Sergei Grudsky
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Pseudoconvex domains spread over complex homogeneous manifolds
, 2012 Using the concept of inner integral curves defined by Hirschowitz we generalize a recent result by Kim, Levenberg and Yamaguchi concerning the obstruction of a pseudoconvex domain spread over a complex homogeneous manifold to be Stein.
A. Borel +23 more
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An exotic calculus of Berezin–Toeplitz operators
Mathematika, Volume 71, Issue 2, April 2025.Abstract We develop a calculus of Berezin–Toeplitz operators quantizing exotic classes of smooth functions on compact Kähler manifolds and acting on holomorphic sections of powers of positive line bundles. These functions (classical observables) are exotic in the sense that their derivatives are allowed to grow in ways controlled by local geometry and ...
Izak Oltman
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Non‐cyclicity and polynomials in Dirichlet‐type spaces of the unit ball
Bulletin of the London Mathematical Society, Volume 56, Issue 12, Page 3905-3919, December 2024.Abstract We give a description of the intersection of the zero set with the unit sphere of a polynomial that is zero‐free in the unit ball of Cn${\mathbb {C}}^n$. This description leads to a necessary condition for a polynomial to be cyclic in Dirichlet‐type spaces of the unit ball.
Dimitrios Vavitsas +1 more
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ON TRACES OF ANALYTIC HERZ AND BLOCH TYPE SPACES IN BOUNDED STRONGLY PSEUDOCONVEX DOMAINS IN C^N
Проблемы анализа, 2014 In our paper we provide some direct extentions of our recent sharp results on traces in the analytic function spaces, which we proved earlier in case of the unit ball in C^n, to the case of the bounded strongly pseudoconvex domains with a smooth boundary.
R. F. Shamoyan, S. M. Kurilenko
doaj
New estimates of Rychkov's universal extension operator for Lipschitz domains and some applications
Mathematische Nachrichten, Volume 297, Issue 4, Page 1407-1443, April 2024.Abstract Given a bounded Lipschitz domain Ω⊂Rn$\Omega \subset \mathbb {R}^n$, Rychkov showed that there is a linear extension operator E$\mathcal {E}$ for Ω$\Omega$, which is bounded in Besov and Triebel‐Lizorkin spaces. In this paper, we introduce some new estimates for the extension operator E$\mathcal {E}$ and give some applications.
Ziming Shi, Liding Yao
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Boundary behavior of the Kobayashi metric near a point of infinite type [PDF]
, 2013 Under a potential-theoretical hypothesis named $f$-Property with $f$ satisfying $\displaystyle\int_t^\infty \dfrac{da}{a f(a)}
Khanh, Tran Vu
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