该文研究Dirichlet及随机Dirichlet级数在水平直线或半直线上的增长性,包含关于Taylor级数的相应结果,例如下列简单结果:设Taylor级数F_(z)=sum from n=0 to ∞有收敛半径∞或1,其中0=μ_0<μ_n↑,μ_n∈N,sum from(1/μ_n)<∞....该文研究Dirichlet及随机Dirichlet级数在水平直线或半直线上的增长性,包含关于Taylor级数的相应结果,例如下列简单结果:设Taylor级数F_(z)=sum from n=0 to ∞有收敛半径∞或1,其中0=μ_0<μ_n↑,μ_n∈N,sum from(1/μ_n)<∞.如果这级数有级ρ(在收敛半径是∞或1时,“级”的意义不同),那么在第一种情形。它在从原点出发的每条射线上有级p;在第二种情形,在单位圆盘的每条射线上有级ρ．展开更多
Some polar coordinates are used to determine the domain and the ball of convergence of a multiple Taylor series. In this domain and in this ball the series converges, converges absolutely and converges uniformly on an...Some polar coordinates are used to determine the domain and the ball of convergence of a multiple Taylor series. In this domain and in this ball the series converges, converges absolutely and converges uniformly on any compact set properties of the series may also be studied. For some random multiple are some corresponding properties. Growth and other Taylor series there展开更多
Some previous results on convergence of Taylor series in C^n [3] are improved by indicating outside the domain of convergence the points where the series diverges and simplifying some proofs. These results contain the...Some previous results on convergence of Taylor series in C^n [3] are improved by indicating outside the domain of convergence the points where the series diverges and simplifying some proofs. These results contain the Cauchy-Hadamard theorem in C. Some Cauchy integral formulas of a holomorphic function on a closed ball in C^n are constructed and the Taylor series expansion is deduced.展开更多
For some random Dirichlet series of order (R) infinite almost surely every horizontal line is a Borel line of order (R) infinite and without exceptional values
Simplify the proof on the domain of convergence of multiple power series and consider the case where some of z1, …, zn are contained only in a finite number of terms of the series. Obtain some results on holomorphic ...Simplify the proof on the domain of convergence of multiple power series and consider the case where some of z1, …, zn are contained only in a finite number of terms of the series. Obtain some results on holomorphic functions in Cn.展开更多
文摘该文研究Dirichlet及随机Dirichlet级数在水平直线或半直线上的增长性,包含关于Taylor级数的相应结果,例如下列简单结果:设Taylor级数F_(z)=sum from n=0 to ∞有收敛半径∞或1,其中0=μ_0<μ_n↑,μ_n∈N,sum from(1/μ_n)<∞.如果这级数有级ρ(在收敛半径是∞或1时,“级”的意义不同),那么在第一种情形。它在从原点出发的每条射线上有级p;在第二种情形,在单位圆盘的每条射线上有级ρ．
文摘Some polar coordinates are used to determine the domain and the ball of convergence of a multiple Taylor series. In this domain and in this ball the series converges, converges absolutely and converges uniformly on any compact set properties of the series may also be studied. For some random multiple are some corresponding properties. Growth and other Taylor series there
文摘Some previous results on convergence of Taylor series in C^n [3] are improved by indicating outside the domain of convergence the points where the series diverges and simplifying some proofs. These results contain the Cauchy-Hadamard theorem in C. Some Cauchy integral formulas of a holomorphic function on a closed ball in C^n are constructed and the Taylor series expansion is deduced.
基金the Doctoral Programme Fundation and by theNational Natural Science Fundation of China
文摘For some random Dirichlet series of order (R) infinite almost surely every horizontal line is a Borel line of order (R) infinite and without exceptional values
文摘Simplify the proof on the domain of convergence of multiple power series and consider the case where some of z1, …, zn are contained only in a finite number of terms of the series. Obtain some results on holomorphic functions in Cn.
