کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6418055 1339319 2015 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Solutions of infinite order differential equations without the grouping phenomenon and a generalization of the Fabry-Pólya theorem
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Solutions of infinite order differential equations without the grouping phenomenon and a generalization of the Fabry-Pólya theorem
چکیده انگلیسی

Let {λn}n=1∞ be a sequence of distinct complex numbers diverging to infinity so that |λn|≤|λn+1| for all n∈N, and let {μn}n=1∞ be a sequence of positive integers. Consider the setΛ:={λ1,λ1,…,λ1︸μ1-times,λ2,λ2,…,λ2︸μ2-times,…,λk,λk,…,λk︸μk-times,…}. Subject to the condition μnlog⁡|λn|/|λn|→0 as n→∞, we prove that all non-entire Taylor-Dirichlet series of the form∑n=1∞(∑k=0μn−1cn,kzk)eλnz,cn,k∈C, have a convex natural boundary if and only if Λ is an interpolating variety for the space of entire functions of infraexponential type A|z|0. Our result is in the spirit of the Fabry-Pólya gap results.We also prove that if Λ is the zero set of some F∈A|z|0 but not an interpolating variety, it is still possible for the solutions of the differential equation of infinite order F(d/dz)f=0 to admit a Taylor-Dirichlet series representation, that is, a representation without groupings.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 423, Issue 2, 15 March 2015, Pages 1825-1837
نویسندگان
,