Natural boundary of random Dirichlet series
نویسندگان
چکیده
منابع مشابه
Natural Boundary of Random Dirichlet Series
For the random Dirichlet series ∞ ∑ n=0 Xn(ω) e−sλn (s = σ + it ∈ C, 0 = λ0 < λn ↑ ∞), whose coefficients are uniformly nondegenerate independent random variables, we provide some explicit conditions for the line of convergence to be its natural boundary a.s. Running Title Natural Boundary of Random Dirichlet Series
متن کاملNatural Boundaries of Dirichlet Series
We prove some conditions on the existence of natural boundaries of Dirichlet series. We show that generically the presumed boundary is the natural one. We also give an application of natural boundaries in determining asymptotic results.
متن کاملJulia Lines of General Random Dirichlet Series
In this paper, we consider a random entire function f(s, ω) defined by a random Dirichlet series ∑∞ n=1Xn(ω)e −λns whereXn are independent and complex valued variables, 0 6 λn ր +∞. We prove that under natural conditions, for some random entire functions of order (R) zero f(s, ω) almost surely every horizontal line is a Julia line without an exceptional value. The result improve a theorem of J....
متن کاملIntegral Means and Boundary Limits of Dirichlet Series
We study the boundary behavior of functions in the Hardy spaces H p for ordinary Dirichlet series. Our main result, answering a question of H. Hedenmalm, shows that the classical F. Carlson theorem on integral means does not extend to the imaginary axis for functions in H ∞, i.e., for ordinary Dirichlet series in H∞ of the right half-plane. We discuss an important embedding problem for H , the ...
متن کاملDirichlet Series
This definition could have been given to an 18th or early 19th century mathematical audience, but it would not have been very popular: probably they would not have been comfortable with the Humpty Dumpty-esque redefinition of multiplication. Mathematics at that time did have commutative rings: rings of numbers, of matrices, of functions, but not rings with a “funny” multiplication operation def...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Ukrainian Mathematical Journal
سال: 2006
ISSN: 0041-5995,1573-9376
DOI: 10.1007/s11253-006-0124-3