Peak Points for Pseudoconvex Domains: A Survey

This paper surveys results concerning peak points for pseudoconvex domains. It includes results of Laszlo that have not been published elsewhere.      

A Remark on Zero and Peak Sets on Weakly Pseudoconvex Domains

Let be a relatively compact, smoothly bounded, pseudoconvexdomain of a Stein manifold, and let A() be the algebra of allcontinuous functions on which are holomorphic on . It is shown that a zero set on for A()is a peak set for A().     

Volume Approximations of Strongly Pseudoconvex Domains

In convex geometry, the Blaschke surface area measure on the boundary of a convex domain can be interpreted in terms of the complexity of approximating polyhedra. This approach is formulated in the holomorphic setting to establish an alternate interpretation of Fefferman’s hypersurface measure on boundaries of strongly pseudoconvex domains in \(\mathbb {C}^2\). In particular, it is shown that Fefferman’s measure can be recovered from the Bergman kernel of the domain.     

Automorphism Group of Toeplitz Algebras on Certain Pseudoconvex Domains

in this paper, we characterize the automorphism groups of Toeplitz algebras oncertain strongly pseudoconvex domains of Cn, and obtain a generalized BDF theorem for aspecial kind of essential normal operator tupies.     

拟凸域上沿某些方向的边界 Schwarz 引理*

本文直接利用全纯映照的性质研究边界Schwarz引理,建立了拟凸域上沿某些满足正定条件的方向的边界Schwarz引理. 文章推广了强拟凸域情形的主要结果,但是证明的方法是不一样的.     

An Embedding Theorem for Pseudoconvex Domains in Banach Spaces

We show that a pseudoconvex open subset of a Banach space with an unconditional basis is biholomorphic to a closed direct submanifold of a Banach space with an unconditional basis.This research supported in part by NSF grant DMS-0203072 and a Bilsland Dissertation Fellowship from the Graduate School of Purdue University. This paper is the result of my thesis research under the direction of László Lempert, and I would like to thank him for his patient and wise guidance. I would also like to thank Andreas Defant and David Pérez-García for their suggestions regarding tensor products and directing me to the paper [4], and Steve Bell for his suggestions.     

无穷维复空间的拟凸Riemann区域(英)

本文利用多极集的测度研究了凸空间上的Riemann区域的拟凸性。     

Inequalities for Eigenvalues of the Sub-Laplacian on Strictly Pseudoconvex CR Manifolds

Mathematical Notes - The sub-Laplacian plays a key role in CR geometry. In this paper, we investigate eigenvalues of the sub-Laplacian on bounded domains of strictly pseudoconvex CR manifolds,...     

Hilbert Geometry for Strictly Convex Domains

We prove in this paper that the Hilbert geometry associated with a bounded open convex domain in R ⁿ whose boundary is a ² hypersuface with nonvanishing Gaussian curvature is bi-Lipschitz equivalent to the n-dimensional hyperbolic space H ⁿ . Moreover, we show that the balls in such a Hilbert geometry have the same volume growth entropy as those in H ⁿ .     

一类拟凸域的不变Khler度量与曲率

本文对Ｃｍ＋ｎ中的一类有界拟凸域给出了不变Ｋｈｌｅｒ度量及其曲率以及不变调和函数的显表达式     

Strictly and Roughly Convexlike Functions

A function is said to be strictly and roughly convexlike with respect to the roughness degree r > 0 (for short, strictly r-convexlike) provided that, for all x ₀, x ₁ D satisfying ||x ₀ – x ₁|| > r, there exists a ]0, 1[ such that

On Analytic Interpolation Manifolds in Boundaries of Weakly Pseudoconvex Domains

Let Ω be a bounded, weakly pseudoconvex domain in C ⁿ , n ≤ 2, with real-analytic boundary. A real-analytic submanifold M ? ?Ω is called an analytic interpolation manifold if every real-analytic function on M extends to a function belonging to (Ω¯). We provide sufficient conditions for M to be an analytic interpolation manifold. We give examples showing that neither of these conditions can be relaxed, as well as examples of analytic interpolation manifolds lying entirely within the set of weakly pseudoconvex points of ?Ω.     

严格 B -预不变凸函数

该文首先得到了严格B -预不变凸函数的一个充分条件,然后给出了严格 B -预不变凸函数的一些性质,最后得到了关于目标函数为严格 B -预不变凸函数的极小化问题的若干结果.     

Singular Strictly Monotone Functions

We describe a universal approach to constructing continuous strictly monotone increasing singular functions on the closed interval [-1,1]. The “generator” of the method is the series ∑_k=1∞±2^-k with random permutation of signs, and the corresponding functions are generated as distribution functions of such series. As examples, we consider two stochastic methods of arranging signs: independent and Markov.     

On the Cauchy Principal Value of the Khenkin-Ramirez Singular Integral in Strictly Pseudoconvex Domains of ℂ <Superscript>n</Superscript>

We show that in the multidimensional case (unlike the complex plane) the Cauchy principal value of the Khenkin-Ramirez singular integral in strictly pseudoconvex domains is equal to the limit value of this integral inside the domain.Original Russian Text Copyright © 2005 Kytmanov A. M. and Myslivets S. G.The first author was supported by a grant of the President of the Russian Federation and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-1212.2003.1); the second author was supported by the Krasnoyarsk Region Science Foundation (Grant 12F0063C).__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 625–633, May–June, 2005.     

Subdifferential Properties of Quasiconvex and Pseudoconvex Functions: Unified Approach

In this paper, we are mainly concerned with the characterization of quasiconvex or pseudoconvex nondifferentiable functions and the relationship between those two concepts. In particular, we characterize the quasiconvexity and pseudoconvexity of a function by mixed properties combining properties of the function and properties of its subdifferential. We also prove that a lower semicontinuous and radially continuous function is pseudoconvex if it is quasiconvex and satisfies the following optimality condition: 0f(x)f has a global minimum at x. The results are proved using the abstract subdifferential introduced in Ref. 1, a concept which allows one to recover almost all the subdifferentials used in nonsmooth analysis.