Results 51 to 60 of about 2,775,649 (193)
Estimates of Invariant Metrics on Pseudoconvex Domains of Finite Type in C3
Abstract and Applied Analysis, 2014 Let Ω be a smoothly bounded pseudoconvex domain in C3 and assume that z0∈bΩ is a point of finite 1-type in the sense of D’Angelo. Then, there are an admissible curve Γ⊂Ω∪{z0}, connecting points q0∈Ω and z0∈bΩ, and a quantity M(z,X), along z∈Γ, which ...
Sanghyun Cho, Young Hwan You
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Variations of pseudoconvex domains
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1983 A connected Hausdorff space E together with a locally homeomorphic map \(\pi\) of E to \({\mathbb{R}}^ m\) is called an unramified covering domain over the space \({\mathbb{R}}^ m\). Suppose D is such a domain and \(D_ p\) is a sequence of relatively compact subdomains of D such that \(x^ 0\in D_ 1\), \(D_ p\subset D_{p+1}\), \(\cup^{\infty}_{p=1}D_ p ...
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Necessary and Sufficient Conditions for Set‐Valued Maps with Set Optimization
Abstract and Applied Analysis, Volume 2018, Issue 1, 2018., 2018 Optimality conditions are studied for set‐valued maps with set optimization. Necessary conditions are given in terms of S‐derivative and contingent derivative. Sufficient conditions for the existence of solutions are shown for set‐valued maps under generalized quasiconvexity assumptions.
Abdessamad Oussarhan +2 more
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On a higher dimensional worm domain and its geometric properties
Journal of the London Mathematical Society, Volume 111, Issue 6, June 2025.Abstract We construct new three‐dimensional variants of the classical Diederich–Fornæss worm domain. We show that they are smoothly bounded, pseudoconvex, and have nontrivial Nebenhülle. We also show that their Bergman projections do not preserve the Sobolev space for sufficiently large Sobolev indices.
Steven G. Krantz +2 more
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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
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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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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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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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On holomorphic mappings of strictly pseudoconvex domains
Sbornik: Mathematics, 2022 We study the boundary regularity of proper holomorphic mappings between strictly pseudoconvex domains with boundaries of class $C^2$. In the second part of the paper we establish an extension of the Wong-Rosay theorem to piecewise smooth strictly pseudoconvex domains. Bibliography: 37 titles.
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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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