布拉施克積的有限多個線性組合在單位圓盤上是均勻稠密在有界的可解析函數代數上。

The finite linear combinations of Blaschke products are uniformly dense in the algebra of bounded analytic functions on the open unit disc.

目錄
0. 前言 ………………………………………………………P.1
1. H^p 空間的定義和基本的性質……………………………P.1
1.1 布拉施克積………………………………………………P.3
1.2 某些位勢論………………………………………………P.9
2. 布拉施克積的有限的線性組合生成 H^infinity………P.11
2.1 Frostman定理……………………………………………P.11
2.2 商布拉施克積……………………………………………P.14
2.3 ㄧ些極值問題……………………………………………P.16
2.4 Marshall定理……………………………………………P.23
參考文獻………………………………………………………P.26

Contents
0. Introduction ……………………………………………P.27
1. Definitions and basic properties of H^p spaces…P.27
1.1 Blaschke products ……………………………………P.29
1.2 Some Potential theory ………………………………P.36
2. Blaschke products as generators of H^infinity…P.38
2.1 Frostman's theorem …………………………………P.38
2.2 On the quotients of Blaschke products …………P.41
2.3 Some Extremal problem ………………………………P.44
2.4 Marshall's theorem …………………………………P.51
References……………………………………………………P.54

[1] L. V. Ahlfors, Complex analysis, 2nd edition., McGraw-Hill, New York, (1966).
[2] R. G. Douglas. Banach algebra techniques in operator theory, 2nd edition,.
Springer-Verlag, (1998).
[3] R. G. Douglas and W. Rudin, Approximation by inner functions, Pacific J.
Math. 31 (1969), 313-320.
[4] P. L. Duren. Theory of Hp spaces, 2nd edition,. Academic Press, New York
(1970).
[5] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York (1981).
[6] J. B. Garnett and A. NICOLAU, Interpolating Blaschke products generate H^infinity,
Pacific J. Math. 173, No. 2, (1996), 501-510.
[7] K. Hoffman. Banach spaces of analytic functions. Prentice-Hall, Englewood
Cliffs, (1965).
[8] D. Marshall, Blaschke products generate H^infinity, Bull. Amer. Math. Soc, 82 (1976),
494-496.
[9] P. Mattila Geometry of sets and measures in Euclidean spaces. Cambridge University
Press, (1995).
[10] W. Rudin. real and complex analysis. McGraw-Hill, New York, (1986).
[11] M. Tsuji. Potential Theory In Modern Function Theory, 2nd edition,. New York,
Chelsea Pub. Co. (1975).