Lectures on The Theory of FunctionsPDF电子书下载

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INTRODUCTION 1

1．Notation 2

2．The inequalities of Holder and Minkowski 4

3．The selection principle 25

4．Theory of functions of a real variable 26

5．Fourier series 49

6．Some theorems of analysis situs (topology) 66

7．Harmonic functions 68

8．The behaviour of certain special functions of a complex variable 91

CHAPTER Ⅰ 103

9．The maximum modulus principle 103

10．Some classical theorems 112

11．Preliminary results on conformal representation 119

12．The theory of the linear function 125

13-16．Riemann＇s existence theorem 130

17．The conformal representation of limit-domains 140

18-20．Boundary problems in conformal representation 143

CHAPTER Ⅱ 152

21．Subharmonic functions 152

22．Subordination 163

23．The＂principle of subordination＂ 171

24-26．The functions P，Q，R (＂Picard＂functions) 185

27．Functions S and S (＂schlicht＂functions) 205

28．Various developments 225

ADDENDA AND CORRIGENDA 233

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