简介
20世纪20年代，芬兰著名数学家R．Nevanlinna创立了亚纯函数Nevanlinna值分布理论．为Dirichlet级数的研究注入了新的活力。30年代，法国著名数学家S．Mandelbrojt与G．Valiron等人首先对Dirichlet级数所定义的整函数的值分布进行研究，开创了Dirichlet级数研究的新方向。50年代初，余家荣先生留法回国，在国内开创了对Dirichlet级数、随机Dirichlet级数定义的解析函数的增长性、值分布及边界性质的研究，引起了国内外数学界的重视。80年代以来，经过以余家荣教授为代表的、以他的众多学生为主的中国数学工作者的努力，在这方面取得了丰富的成果，使我国在该领域的研究得到国际的重视。
LaDlace—Stieltjes变换是一类在理论和应用上都十分重要的函数，在某种意义上，Dirichlet级数可以看作是它的一种特例。同时Laplace—Stiehjes变换也是Laplace变换的推广，而后者在通信传播技术等方面有广泛的应用，故其研究有助于应用学科的发展。对于这类函数的分析性质的研究，可追溯到20世纪30年代。1963年余家荣教授首先对LaDlace—Stieltjes变换定义的整函数的增长性及值分布方面的研究作了一些奠基性工作。近年来，c．J．K．Batty、高宗升、尚丽娜和作者等人继续对这类函数作了研究，取得了一些很好的结果。
《On the Growth of Laplace-Stieltjes Transforms and the Singular Direction of Complex Analysis》以作者的研究X-作为基础，前两章主要介绍关于Laplace二Stieltjes变换增长性的研究工作，中间两章讨论了复函数奇异方向的研究工作，都有很重要的意义。最后一章介绍Dirichlet级数最新的研究成果，有很大的研究价值。《On the Growth of Laplace-Stieltjes Transforms and the Singular Direction of Complex Analysis》为有志探讨单复变函数值分布理论，尤其是Dirichlet级数的学者提供了一个新的参考和一个新的研究途径。凡具备“复变函数”和“实变函数”等大学本科知识的读者，都可以读懂《On the Growth of Laplace-Stieltjes Transforms and the Singular Direction of Complex Analysis》。
目录
序
Preface
Chapter 1 On the growth of the Laplace-Stieltjes transform convergent in the complex plane
1.1 Entire functions represented by L-S transform
1.2 On orders and types of L-S transform convergent in the complex plane
1.3 On Type-function of L-S transform convergent in the complex plane
1.4 Abscissas of convergence of L-S transform independent of { An }
Chapter 2 On the growth of the Laplace-Stieltjes transform convergent in the right half plane
2.1 On Type-function of L-S transform convergent in the right half-plane
2.2 On the growth of zero order L-S transform convergent in the right half-plane
2.3 The L-S transform convergent in the right half-plane and its relative transform
2.4 The value distribution of the L-S transform convergent in the fight half-plane
Chapter 3 Singular directions of quasimeromorphic mappings
3.1 Introduction and some definitions
3.2 A singular direction of quasimeromorphie mappings on some Type-functions in the complex plane
3.3 A singular radius of quasimeromorphic mappings on some Type-functions in the unit disc
3.4 On the filling discs in Borel radius of quasimeromorphic mapping in the unit disc
3.5 On Nevanlinna direction and Julia direction of quasimeromorphic mappings
Chapter 4 The growth of algehroidal functions
4.1 Introduction of algebroidal functions
4.2 A connection between the Nevanlinna characteristic function and-the maximum modulus of algebroidal functions
4.3 Some properties of algebroidal function
4.4 On filling discs in the strong Borel direction of the algebroidal function with finite order
4.5 On T-radius of algebroidal function in the unit disc
4.6 Algebroidal function and its derivate function in the unit disc
4.7 Normality criteria for families of algebroidal functions
Chapter 5 Some new studies of Diriehlet series and random Diriehlet series
5.1 Introduction and background
5.2 On orders and types of Dirichlet series of slow growth
5.3 On orders and types of random Dirichlet series of slow growth
5.4 On the distribution of random Dirichlet series in the whole plane
5.5 Pits on some entire functions defined by. Dirichlet series
5.6 On some q-orders and q-types of Dirichlet-Hadamard product function
Bibliography
Index
后记
Preface
Chapter 1 On the growth of the Laplace-Stieltjes transform convergent in the complex plane
1.1 Entire functions represented by L-S transform
1.2 On orders and types of L-S transform convergent in the complex plane
1.3 On Type-function of L-S transform convergent in the complex plane
1.4 Abscissas of convergence of L-S transform independent of { An }
Chapter 2 On the growth of the Laplace-Stieltjes transform convergent in the right half plane
2.1 On Type-function of L-S transform convergent in the right half-plane
2.2 On the growth of zero order L-S transform convergent in the right half-plane
2.3 The L-S transform convergent in the right half-plane and its relative transform
2.4 The value distribution of the L-S transform convergent in the fight half-plane
Chapter 3 Singular directions of quasimeromorphic mappings
3.1 Introduction and some definitions
3.2 A singular direction of quasimeromorphie mappings on some Type-functions in the complex plane
3.3 A singular radius of quasimeromorphic mappings on some Type-functions in the unit disc
3.4 On the filling discs in Borel radius of quasimeromorphic mapping in the unit disc
3.5 On Nevanlinna direction and Julia direction of quasimeromorphic mappings
Chapter 4 The growth of algehroidal functions
4.1 Introduction of algebroidal functions
4.2 A connection between the Nevanlinna characteristic function and-the maximum modulus of algebroidal functions
4.3 Some properties of algebroidal function
4.4 On filling discs in the strong Borel direction of the algebroidal function with finite order
4.5 On T-radius of algebroidal function in the unit disc
4.6 Algebroidal function and its derivate function in the unit disc
4.7 Normality criteria for families of algebroidal functions
Chapter 5 Some new studies of Diriehlet series and random Diriehlet series
5.1 Introduction and background
5.2 On orders and types of Dirichlet series of slow growth
5.3 On orders and types of random Dirichlet series of slow growth
5.4 On the distribution of random Dirichlet series in the whole plane
5.5 Pits on some entire functions defined by. Dirichlet series
5.6 On some q-orders and q-types of Dirichlet-Hadamard product function
Bibliography
Index
后记
- 名称
- 类型
- 大小
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