On generalized pseudoconvex functions
نویسندگان
چکیده
منابع مشابه
On Holomorphic L2 functions on Coverings of Strongly Pseudoconvex Manifolds
In this paper we answer an important question posed in the paper [GHS] by Gromov, Henkin and Shubin on existence of sufficiently many holomorphic L2 functions on arbitrary coverings of strongly pseudoconvex manifolds.
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In this paper we will show how to construct holomorphic Lp-functions on unbranched coverings of strongly pseudoconvex manifolds. Also, we prove some extension and approximation theorems for such functions.
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1. Let M be a complex manifold with a smooth boundary which will be denoted bM , dim C M = n. Let us denote M = M ∪ bM and assume for simplicity that M ⊂ ˜ M where˜M is a complex neighbourhood of M , dim C ˜ M = n, so that every point z ∈ bM is an interior point of˜M. Let us take a C ∞-function ρ : ˜ M → R such that M = z | ρ(z) < 0 , bM = z | ρ(z) = 0 ; dρ(z) = 0 for all z ∈ bM. (0.1) For any ...
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First order characterizations of pseudoconvex functions are investigated in terms of generalized directional derivatives. A connection with the invexity is analysed. Well-known first order characterizations of the solution sets of pseudolinear programs are generalized to the case of pseudoconvex programs. The concepts of pseudoconvexity and invexity do not depend on a single definition of the g...
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We define the algebra G̃(A) of Colombeau generalized functions on a subset A of the space of generalized points R̃d. If A is an open subset of R̃d, such generalized functions can be identified with pointwise maps from A into the ring of generalized numbers C̃. We study analyticity in G̃(A), where A is an open subset of C̃. In particular, if the domain is an open ball for the sharp norm on C̃, we chara...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1989
ISSN: 0022-247X
DOI: 10.1016/0022-247x(89)90339-9