Some theorems on bounded holomorphic functions
نویسندگان
چکیده
منابع مشابه
Bounded Holomorphic Functions on Bounded Symmetric Domains
Let D be a bounded homogeneous domain in C , and let A denote the open unit disk. If z e D and /: D —► A is holomorphic, then ß/(z) is defined as the maximum ratio \Vz(f)x\/Hz(x, 3c)1/2 , where x is a nonzero vector in C and Hz is the Bergman metric on D . The number ßf(z) represents the maximum dilation of / at z . The set consisting of all ß/(z), for z e D and /: D —► A holomorphic, is known ...
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Let G be a region in the complex plane such that there is a nonconstant bounded holomorphic function on G, and denote the algebra of all such functions by BH{G). Let H^{G) denote the Banach algebra that arises when BH{G) is endowed with the supremum norm. In the case where G is the unit disc D, H*>(G) has been extensively studied, mostly by a real-variables analysis of the radial boundary value...
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We organize this set of notes around a few theorems of Weierstrass. Write OCn for the sheaf of holomorphic functions on C. In the first three sections, we deduce the following “algebraic” results as consequences of the Weierstrass theorems: (i) for each open set Ω ⊂ C, the ring OCn(Ω) is not Noetherian, (ii) the local ring OCn,0 is factorial, (iii) the local ring OCn,0 is Noetherian. The two la...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1964
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1964-11124-1