Tauberian Theorems for the Laplace-Stieltjes Transform
نویسندگان
چکیده
منابع مشابه
Tauberian-type theorems with application to the Stieltjes transformation
The Abelian and Tauberian-type theorems were introduced by Stanković [7] and Pilipović et al. [5]. In the first part of this paper, we give the definition of the quasiasymptotic expansion at 0+ and the quasiasymptotic behaviour of distributions at infinity from S′+ introduced in [1]. In this paper, we give the definition of space L′(r), classical Stieltjes transformation, modified Stieltjes tra...
متن کاملA generalization of Littlewood's Tauberian theorem for the Laplace transform
In this paper we will consider a Tauberian problem of the following kind: Suppose that and are two functions of bounded variation on any nite interval 0; T]; T > 0, and suppose that (0) = (0) = 0. If furthermore Z 1 0 e ?st dd(t) Z 1 0 e ?st dd(t); s ! 0+; (0.1) where satisses some kind of regularity condition and satisses a Tauberian condition, then (t) (t); t ! 1: (0.2) Here (0.2) means that ...
متن کاملTauberian 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 کاملTauberian 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 کاملThe Cayley Hamilton and Frobenius Theorems via the Laplace Transform
The Cayley Hamilton theorem on the characteristic polynomial of a matrix A and Frobenius’ theorem on minimal polynomial of A are deduced from the familiar Laplace transform formula L(eAt) = (sI − A)−1. This formula is extended to a formal power series ring over an algebraically closed field of characteristic 0, so that the argument applies in the more general setting of matrices over a field of...
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: Transactions of the American Mathematical Society
سال: 1990
ISSN: 0002-9947
DOI: 10.2307/2001725