Approximation by entire functions in the mean on the real line

1991 ◽  
Vol 43 (1) ◽  
pp. 100-104 ◽  
Author(s):  
A. I. Stepanets ◽  
N. I. Stepanets
Keyword(s):  
Real Line ◽  
Entire Functions ◽  
The Real ◽  
The Mean

scholarly journals Weighted approximation by entire functions interpolating at finitely or infinitely many points on the real line

2009 ◽  
Vol 25 (3) ◽  
pp. 303-310
Author(s):  
Biancamaria Della Vecchia ◽  
Giuseppe Mastroianni ◽  
József Szabados
Keyword(s):  
Real Line ◽  
Entire Functions ◽  
Weighted Approximation ◽  
The Real

scholarly journals A Generalized Telegraph Process with Velocity Driven by Random Trials

2013 ◽  
Vol 45 (04) ◽  
pp. 1111-1136 ◽  
Author(s):  
Irene Crimaldi ◽  
Antonio Di Crescenzo ◽  
Antonella Iuliano ◽  
Barbara Martinucci
Keyword(s):  
Real Line ◽  
Counting Process ◽  
Bernoulli Trials ◽  
Exponential Distributions ◽  
The Real ◽  
Telegraph Process ◽  
Nonzero Mean ◽  
The Mean ◽  
Moving Particle ◽  
Random Trial

We consider a random trial-based telegraph process, which describes a motion on the real line with two constant velocities along opposite directions. At each epoch of the underlying counting process the new velocity is determined by the outcome of a random trial. Two schemes are taken into account: Bernoulli trials and classical Pólya urn trials. We investigate the probability law of the process and the mean of the velocity of the moving particle. We finally discuss two cases of interest: (i) the case of Bernoulli trials and intertimes having exponential distributions with linear rates (in which, interestingly, the process exhibits a logistic stationary density with nonzero mean), and (ii) the case of Pólya trials and intertimes having first gamma and then exponential distributions with constant rates.

scholarly journals Entire functions mapping countable dense subsets of the reals onto each other monotonically

1974 ◽  
Vol 10 (1) ◽  
pp. 67-70 ◽  
Author(s):  
Daihachiro Sato ◽  
Stuart Rankin
Keyword(s):  
Entire Function ◽  
Real Line ◽  
Entire Functions ◽  
Transcendental Entire Function ◽  
The Real

It is shown that for arbitrary countable dense ssets A and B of the real line, there exists a transcendental entire function whose restriction to the real line is a real-valued strictly monotone increasing surjection taking A onto B The technique used is a modification of the procedure Maurer used to show that for countable dense subsets A and B of the plane, there exists a transcendental entire function whose restriction to A is a bijection from A to B.

scholarly journals Mean Convergence of Entire Interpolations in Weighted Space

2021 ◽  
Vol 15 (5) ◽  
Author(s):  
Felipe Gonçalves ◽  
Friedrich Littmann
Keyword(s):  
Exponential Type ◽  
Real Line ◽  
Weighted Space ◽  
Entire Functions ◽  
The Real ◽  
Target Weight ◽  
Mean Convergence ◽  
Power Weights ◽  
Hermite Interpolations

AbstractWe investigate the convergence of entire Lagrange interpolations and of Hermite interpolations of exponential type $$\tau $$ τ , as $$\tau \rightarrow \infty $$ τ → ∞ , in weighted $$L^p$$ L p -spaces on the real line. The weights are reciprocals of entire functions that depend on $$\tau $$ τ and may be viewed as smoothed versions of a target weight w. The convergence statements are obtained from weighted Marcinkiewicz inequalities for entire functions. We apply our main results to deal with power weights.

Approximation of locally integrable functions on the real line

2014 ◽  
Vol 12 (05) ◽  
pp. 1461002
Author(s):  
Xirong Chang
Keyword(s):  
Exponential Type ◽  
Real Line ◽  
Entire Functions ◽  
The Real ◽  
Integrable Functions ◽  
Functions Of Exponential Type

The aim of this paper is to extend (ψ, β)-derivatives to [Formula: see text]-derivatives for locally integrable functions on the real line and then investigate problems of approximation of the classes of functions determined by these derivatives with the use of entire functions of exponential type.

Behavior on the real line of entire functions represented by Dirichlet series

1991 ◽  
Vol 43 (2) ◽  
pp. 234-238 ◽  
Author(s):  
B. V. Vinnitskii ◽  
V. M. Sorokivskii
Keyword(s):  
Dirichlet Series ◽  
Real Line ◽  
Entire Functions ◽  
The Real

scholarly journals A Generalized Telegraph Process with Velocity Driven by Random Trials

2013 ◽  
Vol 45 (4) ◽  
pp. 1111-1136 ◽  
Author(s):  
Irene Crimaldi ◽  
Antonio Di Crescenzo ◽  
Antonella Iuliano ◽  
Barbara Martinucci
Keyword(s):  
Real Line ◽  
Counting Process ◽  
Bernoulli Trials ◽  
Exponential Distributions ◽  
The Real ◽  
Telegraph Process ◽  
Nonzero Mean ◽  
The Mean ◽  
Moving Particle ◽  
Random Trial

We consider a random trial-based telegraph process, which describes a motion on the real line with two constant velocities along opposite directions. At each epoch of the underlying counting process the new velocity is determined by the outcome of a random trial. Two schemes are taken into account: Bernoulli trials and classical Pólya urn trials. We investigate the probability law of the process and the mean of the velocity of the moving particle. We finally discuss two cases of interest: (i) the case of Bernoulli trials and intertimes having exponential distributions with linear rates (in which, interestingly, the process exhibits a logistic stationary density with nonzero mean), and (ii) the case of Pólya trials and intertimes having first gamma and then exponential distributions with constant rates.

scholarly journals Heteroclinic Solutions for Classical and Singular ϕ-Laplacian Non-Autonomous Differential Equations

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 22 ◽  
Author(s):  
Feliz Minhós
Keyword(s):  
Real Line ◽  
Mean Curvature ◽  
Curvature Operator ◽  
Type Condition ◽  
The Real ◽  
Carathéodory Function ◽  
Mean Curvature Operator ◽  
The Mean ◽  
Autonomous Differential Equations ◽  
Laplacian Equations

In this paper, we consider the second order discontinuous differential equation in the real line, a t , u ϕ u ′ ′ = f t , u , u ′ , a . e . t ∈ R , u ( − ∞ ) = ν − , u ( + ∞ ) = ν + , with ϕ an increasing homeomorphism such that ϕ ( 0 ) = 0 and ϕ ( R ) = R , a ∈ C ( R 2 , R ) with a ( t , x ) > 0 for ( t , x ) ∈ R 2 , f : R 3 → R a L 1 -Carathéodory function and ν − , ν + ∈ R such that ν − < ν + . The existence and localization of heteroclinic connections is obtained assuming a Nagumo-type condition on the real line and without asymptotic conditions on the nonlinearities ϕ and f . To the best of our knowledge, this result is even new when ϕ ( y ) = y , that is for equation a t , u ( t ) u ′ ( t ) ′ = f t , u ( t ) , u ′ ( t ) , a . e . t ∈ R . Moreover, these results can be applied to classical and singular ϕ -Laplacian equations and to the mean curvature operator.

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