Results 41 to 50 of about 579 (168)

CR$CR$ analysis via local uniform completion, a sharp maximum modulus principle and holomorphic extension

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
wiley   +1 more source

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
wiley   +1 more source

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
wiley   +1 more source

Regularity of varieties in strictly pseudoconvex domains [PDF]

, 1988
We prove a theorem on the boundary regularity of a purely p-dimensional complex subvariety of a relatively compact, strictly pseudoconvex domain in a Stein manifold. Some applications describing the structure of the polynomial hull of closed curves in C"
Forstneric, Franc, F. Forstneric
core   +1 more source

Compactness of the canonical solution operator on Lipschitz q-pseudoconvex boundaries

Electronic Journal of Differential Equations, 2019
Let $\Omega\subset\mathbb{C}^n$ be a bounded Lipschitz q-pseudoconvex domain that admit good weight functions. We shall prove that the canonical solution operator for the $\overline{\partial}$-equation is compact on the boundary of $\Omega$ and is ...
Sayed Saber
doaj  

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, Konstantinos Zarvalis   +1 more
wiley   +1 more source

Golden Angle Modulation in Complex Dimension Two

Mathematics
In this paper, we propose a new geometric-shaping design for golden angle modulation (GAM) based on the complex geometric properties of open symmetrized bidisc, termed Bd-GAM, for future generation wireless communication systems.
Kejia Hu, Hongyi Li, Di Zhao, Yuan Jiang
doaj   +1 more source

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
wiley   +1 more source

Toeplitz Algebras on Strongly Pseudoconvex Domains [PDF]

Nagoya Mathematical Journal, 2007
AbstractIn the present paper, it is proved that theK0-group of a Toeplitz algebra on any strongly pseudoconvex domain is always isomorphic to theK0-group of the relative continuous function algebra, and is thus isomorphic to the topologicalK0-group of the boundary of the relative domain.
openaire   +2 more sources

Closed 3‐forms in five dimensions and embedding problems

Journal of the London Mathematical Society, Volume 109, Issue 4, April 2024.
Abstract We consider the question if a five‐dimensional manifold can be embedded into a Calabi–Yau manifold of complex dimension 3 such that the real part of the holomorphic volume form induces a given closed 3‐form on the 5‐manifold. We define an open set of 3‐forms in dimension five which we call strongly pseudoconvex, and show that for closed ...
Simon Donaldson, Fabian Lehmann
wiley   +1 more source