Hardy Classes on Infinitely Connected Riemann Surfaces

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Springer, Nov 14, 2006 - Mathematics - 282 pages
 

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Contents

A QUICK REVIEW
1
Differentials
9
MULTIPLICATIVE ANALYTIC FUNCTIONS
23
Lattice Structure of Harmonic Functions
33
MARTIN COMPACTIFICATION
39
Fine Limits L 9
49
HARDY CLASSES
64
CHAPTER W RIEMANN SURFACES OF PARREAUWIDOM TYPE
83
SHIFTINVARTANT SUBS PACES
160
CHARACTERIZATION OF SURFACES OF PARREAUWIDOM TYPE
179
Conditions Equivalent to the Direct Cauchy Theorem l 38
198
EXAMPLES OF SURFACES OF PARREAUWIDOM TYPE
208
Plane Regions of ParreauWidom Type for Which DCT Fails
215
Further Properties of PWS e g
221
The Corona Problem for PWS
227
CLASSIFICATION OF PEANE REGIONS
234

Proof of Widoms Theorem II
99
CHAPTER WI GREEN LINES
119
The Green Lines and the Martin Boundary I 32
132
CAUCHY THEOREMS
144
The Direct Cauchy Theorem 1 5 I
151
Classification of Plane Regions 25 3
253
APPENDICES
262
References
272
Index
278
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