scholarly journals Open Whitney umbrellas are locally polynomially convex

2016 ◽  
Vol 144 (12) ◽  
pp. 5319-5332
Author(s):  
Octavian Mitrea ◽  
Rasul Shafikov
Keyword(s):  
Polynomially Convex

scholarly journals Polynomially convex hulls of families of arcs

2004 ◽  
Vol 165 (1) ◽  
pp. 1-17
Author(s):  
Zbigniew Słodkowski
Keyword(s):  
Convex Hulls ◽  
Polynomially Convex

scholarly journals The topology of rationally and polynomially convex domains

2014 ◽  
Vol 199 (1) ◽  
pp. 215-238 ◽  
Author(s):  
Kai Cieliebak ◽  
Yakov Eliashberg
Keyword(s):  
Convex Domains ◽  
Polynomially Convex

scholarly journals A new class of polynomially convex sets

1991 ◽  
Vol 29 (1-2) ◽  
pp. 51-62 ◽  
Author(s):  
F. Forstnerič ◽  
E. L. Stout
Keyword(s):  
Convex Sets ◽  
New Class ◽  
Polynomially Convex

scholarly journals A Characterization of Polynomially Convex Sets in Banach Spaces

2017 ◽  
Vol 72 (4) ◽  
pp. 2013-2021
Author(s):  
Mortaza Abtahi ◽  
Sara Farhangi
Keyword(s):  
Banach Spaces ◽  
Convex Sets ◽  
Polynomially Convex

Carleman Approximation by Entire Functions on the Union of Two Totally Real Subspaces of Cn

1994 ◽  
Vol 37 (4) ◽  
pp. 522-526
Author(s):  
Per E. Manne
Keyword(s):  
Entire Functions ◽  
Continuous Functions ◽  
Real Dimension ◽  
Carleman Approximation ◽  
Polynomially Convex ◽  
Cauchy Riemann ◽  
Totally Real

AbstractLet L1, L2 ⊂ Cn be two totally real subspaces of real dimension n, and such that L1 ∩ L2 = {0}. We show that continuous functions on L1 ∪L2 allow Carleman approximation by entire functions if and only if L1 ∪L2 is polynomially convex. If the latter condition is satisfied, then a function f:L1 ∪L2 —> C such that f|LiCk(Li), i = 1,2, allows Carleman approximation of order k by entire functions if and only if f satisfies the Cauchy-Riemann equations up to order k at the origin.

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