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Media type:
E-Article
Title:
A CAUCHY-RIEMANN EQUATION FOR GENERALIZED ANALYTIC FUNCTIONS
Contributor:
WERMER, JOHN
Published:
American Mathematical Society, 2010
Published in:
Proceedings of the American Mathematical Society, 138 (2010) 5, Seite 1667-1672
Language:
English
ISSN:
0002-9939;
1088-6826
Origination:
Footnote:
Description:
<p>We denote by T² the torus: z = exp iθ, w = exp iφ, and we fix a positive irrational number α. $A_{\alpha}$ denotes the space of continuous functions f on T² whose Fourier coefficient sequence is supported by the lattice half-plane n + mα ≥ 0. R. Arens and I. Singer introduced and studied the space $A_{\alpha}$, and it turned out to be an interesting generalization of the disk algebra. Here we construct a differential operator $X_{\Sigma}$ on a certain 3-manifold $\Sigma _{0}$ such that $X_{\Sigma}$ characterizes $A_{\alpha}$ in a manner analogous to the characterization of the disk algebra by the Cauchy-Riemann equation in the disk.</p>