Growth of transcendental entire functions on algebraic varieties |
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Authors: | Stanley M. Einstein-Matthews Clement H. Lutterodt |
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Affiliation: | (1) Department of mathematics, Howard University, 2441 6th. Street, N.W., 20059 Washington, DC, USA |
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Abstract: | LetX be a complete intersection algebraic variety of codimensionm>1 in ℂ m+n . We define the notion of (p,q)-order and (p,q)-K-type for transcendental entire functionsfεO(ℂ m+n ) whereK is a non-pluripolar compact subset of ℂ m+n . Further, we consider the analogues of (p,q)-order and (p,q)-K-type inO(X). We discuss the series expansions of the functions inO(X) in terms of an orthogonal basis in a Hilbert spaceL 2(X, μ), where μ is a capacitary extremal measure onK. Author is grateful to the NSA for partial support during the period of this research. |
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