اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe spectrum of the Leray transform for convex Reinhardt domains in $mathbb C^2$
212
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The Leray transform and related boundary operators are studied for a class of convex Reinhardt domains in $mathbb C^2$. Our class is self-dual; it contains some domains with less than $C^2$-smooth boundary and also some domains with smooth boundary and degenerate Levi form. $L^2$-regularity is proved, and essential spectra are computed with respect to a family of boundary measures which includes surface measure. A duality principle is established providing explicit unitary equivalence between operators on domains in our class and operators on the corresponding polar domains. Many of these results are new even for the classical case of smoothly bounded strongly convex Reinhardt domains.
قيم البحث
اقرأ أيضاً
We compute the exact norms of the Leray transforms for a family $mathcal{S}_{beta}$ of unbounded hypersurfaces in two complex dimensions. The $mathcal{S}_{beta}$ generalize the Heisenberg group, and provide local projective approximations to any smoo
th, strongly $mathbb{C}$-convex hypersurface $mathcal{S}_{beta}$ to two orders of tangency. This work is then examined in the context of projective dual $CR$-structures and the corresponding pair of canonical dual Hardy spaces associated to $mathcal{S}_{beta}$, leading to a universal description of the Leray transform and a factorization of the transform through orthogonal projection onto the conjugate dual Hardy space.
We give a complete characterization of those disk bundles over surfaces which embed as rationally convex strictly pseudoconvex domains in $mathbb{C}^2$. We recall some classical obstructions and prove some deeper ones related to symplectic and contac
t topology. We explain the close connection to Lagrangian surfaces with isolated singularities and develop techniques for constructing such surfaces. Our proof also gives a complete characterization of Lagrangian surfaces with open Whitney umbrellas, answering a question first posed by Givental in 1986.
We study the homeomorphic extension of biholomorphisms between convex domains in $mathbb C^d$ without boundary regularity and boundedness assumptions. Our approach relies on methods from coarse geometry, namely the correspondence between the Gromov b
oundary and the topological boundaries of the domains and the dynamical properties of commuting 1-Lipschitz maps in Gromov hyperbolic spaces. This approach not only allows us to prove extensions for biholomorphisms, but for more general quasi-isometries between the domains endowed with their Kobayashi distances.
Let $Omega$ be a bounded Reinhardt domain in $mathbb{C}^n$ and $phi_1,ldots,phi_m$ be finite sums of bounded quasi-homogeneous functions. We show that if the product of Toeplitz operators $T_{phi_m}cdots T_{phi_1}=0$ on the Bergman space on $Omega$, then $phi_j=0$ for some $j$.
We obtain explicit bounds on the difference between local and global Kobayashi distances in a domain of $mathbb C^n$ as the points go toward a boundary point with appropriate geometric properties. We use this for the global comparison of various inva
riant distances. We provide some sharp estimates in dimension $1$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
