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

Published online by Cambridge University Press:  20 November 2018

Per E. Manne
Per E. Manne*
Affiliation:
Department of Mathematics, Norwegian School of Economics and Business Administration N-5035 Bergen-Sandviken Norway
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Abstract

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Let L 1, L 2 ⊂ Cn be two totally real subspaces of real dimension n, and such that L 1 ∩ L 2 = {0}. We show that continuous functions on L 1 ∪L 2 allow Carleman approximation by entire functions if and only if L 1 ∪L 2 is polynomially convex. If the latter condition is satisfied, then a function f:L 1 ∪L 2 —> C such that f|L iCk(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.

Keywords

32E30

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 4 , 01 December 1994 , pp. 522 - 526
Copyright
Copyright © Canadian Mathematical Society 1994

References

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