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1970 University A(Un absolute value Amer Math Soc analytic functions analytic varieties Banach Beurling bilinear map Blaschke products Bochner boundary values bounded functions holomorphic Bull Amer Math Cantor set compact subset complex variables consider convex function define denote domain of holo entire functions example exist bounded functions false Forelli Forelli's Theorem Fourier analysis Fourier Series function f function in H Function Theory Functional Analysis given growth conditions H*3 spaces holomorphic function Hp(Un i|i o p implies inner function interPolation set intersection invariant subspace Jensen's inequality Let f log|2n h Log|f|dm Math Soc 13 maximal ideal space measure is zero monomial non-negative open problem open set outer function PI set Poisson integral Polydisc algebras Proc Amer Math proof quotient Riesz Rudin set of f sheaf theory slice function Stone-Weierstrass Theorem theorem of Beurling's third quadrants torus whose Fourier unit disk unit vector zero free function