Integrability theorems for power series I. Tauberian theorems

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Regularization of Divergent Series and Tauberian Theorems

The concepts of convergence and divergence, while not defined explicitly until early 19th century, have been studied since the third century BC. Throughout this time, mathematicians have largely focused upon convergent sequences and series, having seemingly little analytical reason to study series that diverged. However, as the area of mathematical analysis developed over the past few centuries...

متن کامل

Tauberian theorems for sum sets

Introduction. The sums formed from the set of non-negative powers of 2 are just the non-negative integers. It is easy to obtain “abelian” results to the effect that if a set is distributed like the powers of 2, then the sum set will be distributed like Dhe non-negative integers. We will be concerned here with converse, or “Tauberian” results. The main theme of this paper is t’he following quest...

متن کامل

Tauberian Theorems for Summability Transforms

we then write sn → s(A), where A is the A method of summability. Appropriate choices of A= [an,k] for n,k ≥ 0 give the classical methods [2]. In this paper, we present various summability analogs of the strong law of large numbers (SLLN) and their rates of convergence in an unified setting, beyond the class of random-walk methods. A convolution summability method introduced in the next section ...

متن کامل

One-sided Tauberian Theorems for Dirichlet Series Methods of Summability

We extend recently established two-sided or O-Tauberian results concerning the summability method Dλ,a based on the Dirichlet series ∑ ane−λnx to one-sided Tauberian results. More precisely, we formulate one-sided Tauberian conditions, under which Dλ,a-summability implies convergence. Our theorems contain various known results on power series methods of summability and, in the so-called high in...

متن کامل

Multidimensional Tauberian Theorems for Vector-valued Distributions

We prove several Tauberian theorems for regularizing transforms of vector-valued distributions. The regularizing transform of f is given by the integral transform M φ(x, y) = (f ∗ φy)(x), (x, y) ∈ R n × R+, with kernel φy(t) = yφ(t/y). We apply our results to the analysis of asymptotic stability for a class of Cauchy problems, Tauberian theorems for the Laplace transform, the comparison of quas...

متن کامل

ذخیره 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: Journal of Mathematical Analysis and Applications

سال: 1961

ISSN: 0022-247X

DOI: 10.1016/0022-247x(61)90070-1