Results 11 to 20 of about 1,091 (210)

The stieltjes transform of distributions [PDF]

International Journal of Mathematics and Mathematical Sciences, 1979
In the present work, two complex inversion formulas of Byrne and Love for generalized Stieltjes transformation are shown to be valid for a class of distributions. This is accomplished by transfering the complex inversion formulas on the testing function space of a class of distributions and then showing that the limiting process in the resulting ...
U. N. Tiwari, J. N. Pandey
doaj   +4 more sources

Necessary and sufficient condition that the limit of Stieltjes transforms is a Stieltjes transform

Journal of Approximation Theory, 2003
The paper deals with the Stieltjes transform \(S_P\) of a probability measure \(P\) defined as the function \(S_P: \{z\in \mathbb{C}:\text{Im}(z)>0\}\to {\mathbb C}\) given by \[ S_P(z)=\int^{\infty}_{-\infty}{\frac{1}{w-z}}dP(w). \] The main result proved in Theorem 1 states that if \((P_n)\) are real Borel probability measures with Stieltjes ...
Geronimo, Jeffrey S., Hill, Theodore P.
exaly   +7 more sources

Laplace-Stieltjes transform of the system mean lifetime via geometric process model

Open Mathematics, 2016
Operation principle of the engineering systems occupies an important role in the reliability theory. In most of the studies, the reliability function of the system is obtained analytically according to the structure of the system.
Gökdere Gökhan, Gürcan Mehmet
doaj   +3 more sources

A Comprehensive Study of Generalized Lambert, Generalized Stieltjes, and Stieltjes–Poisson Transforms

Axioms
In this paper, we explore the properties of the generalized Lambert transform, the L-transform, the generalized Stieltjes transform, and the Stieltjes–Poisson transform within the framework of Lebesgue spaces.
Jeetendrasingh Maan, E. R. Negrín
doaj   +4 more sources

The approximation of Laplace-Stieltjes transforms with finite order. [PDF]

J Inequal Appl, 2017
In this paper, we study the irregular growth of an entire function defined by the Laplace-Stieltjes transform of finite order convergent in the whole complex plane and obtain some results about λ-lower type.
Xu HY, Liu SY.
europepmc   +3 more sources

Recent developments on the Stieltjes transform of generalized functions [PDF]

International Journal of Mathematics and Mathematical Sciences, 1987
This paper is concerned with recent developments on the Stieltjes transform of generalized functions. Sections 1 and 2 give a very brief introduction to the subject and the Stieltjes transform of ordinary functions with an emphasis to the inversion ...
Ram Sankar Pathak, Lokenath Debnath
doaj   +2 more sources

The growth and approximation for an analytic function represented by Laplace-Stieltjes transforms with generalized order converging in the half plane. [PDF]

J Inequal Appl, 2018
By utilizing the concept of generalized order, we investigate the growth of Laplace–Stieltjes transform converging in the half plane and obtain one equivalence theorem concerning the generalized order of Laplace–Stieltjes transforms.
Xu HY, Wang H.
europepmc   +2 more sources

Growth and Approximation of Laplace-Stieltjes Transform with p,q-Proximate Order Converges on the Whole Plane

Journal of Function Spaces, 2020
One purpose of this paper is to study the growth of entire functions defined by Laplace-Stieltjes transform converges on the whole complex plane, by introducing the concept of p,q-proximate order, and one equivalence theorem of the p,q-proximate order of
Yong Qin Cui, Hong Yan Xu
doaj   +2 more sources

The Growth of Entire Functions Defined by Laplace–Stieltjes Transforms Related to Proximate Order and Approximation

Journal of Function Spaces, 2020
In this article, we discuss the growth of entire functions represented by Laplace–Stieltjes transform converges on the whole complex plane and obtain some equivalence conditions about proximate growth of Laplace–Stieltjes transforms with finite order and
Wen Ju Tang, Jian Chen, Hong Yan Xu
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Abelian theorems for the stieltjes transform of functions, II [PDF]

International Journal of Mathematics and Mathematical Sciences, 1981
An initial (final) value Abelian theorem concerning transforms of functions is a result in which known behavior of the function as its domain variable approaches zero (approaches ∞) is used to infer the behavior of the transform as its domain variable ...
Richard D. Carmichael, Elmer K. Hayashi
doaj   +2 more sources