Growth of transcendental entire functions on algebraic varieties

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.