This note implies only a moment condition upon the coefficients of random Dirichlet series to study the convergence and growth of the series. The condition needs the coefficients to satisfy the so-called inverse H?lde...This note implies only a moment condition upon the coefficients of random Dirichlet series to study the convergence and growth of the series. The condition needs the coefficients to satisfy the so-called inverse H?lder inequality, which need not be independent. The note uses a method whose feature is to compare the convergence of two series, and obtains two theorems, one dealing with the convergence of the random Dirichlet series, another the growth of the random analytic function represented by the series. These results can be used to improve essentially some known conclusions.展开更多
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
文摘This note implies only a moment condition upon the coefficients of random Dirichlet series to study the convergence and growth of the series. The condition needs the coefficients to satisfy the so-called inverse H?lder inequality, which need not be independent. The note uses a method whose feature is to compare the convergence of two series, and obtains two theorems, one dealing with the convergence of the random Dirichlet series, another the growth of the random analytic function represented by the series. These results can be used to improve essentially some known conclusions.
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．
