Weighted Lacunary Interpolation Processes On An Infinite Interval - Couverture souple

Mathur, Pankaj

 
9783845474908: Weighted Lacunary Interpolation Processes On An Infinite Interval
Couverture souple
ISBN 10 : 3845474904 ISBN 13 : 9783845474908
Editeur : LAP LAMBERT Academic Publishing, 2013

Synopsis

The aim of this book is to study certain weighted lacunary interpolation processes on an infinite interval. By lacunary interpolation we mean to study an interpolation process when non consecutive derivatives are prescribed on a given set of nodes. Here we have considered the existence, uniqueness, explicit representation of a modified weighted (0, 1, 3) and (0, 1, 2, … , r - 2, r) interpolations on an arbitrary set of nodes, weighted (0, 2), (0, 1, 3) interpolations on the zeros of nth-Hermite polynomial and a mixed type (0; 0, 2) interpolation when function values and weighted (0, 2) are prescribed on the zeros of nth-Hermite polynomials and its derivative respectively. A convergence theorem has been obtained in these cases. The results obtained here are better to some earlier results obtained by several mathematicians in the sense that (i) an artificial looking condition, used for obtaining the explicit representation of the fundamental polynomials, has been replaced by a simple interpolatory condition (ii) the results have been obtained in the case when n is considered to be odd and (iii) an improved quantitative estimate of the interpolatory polynomials has been obtained.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

The aim of this book is to study certain weighted lacunary interpolation processes on an infinite interval. By lacunary interpolation we mean to study an interpolation process when non consecutive derivatives are prescribed on a given set of nodes. Here we have considered the existence, uniqueness, explicit representation of a modified weighted (0, 1, 3) and (0, 1, 2, ... , r - 2, r) interpolations on an arbitrary set of nodes, weighted (0, 2), (0, 1, 3) interpolations on the zeros of nth-Hermite polynomial and a mixed type (0; 0, 2) interpolation when function values and weighted (0, 2) are prescribed on the zeros of nth-Hermite polynomials and its derivative respectively. A convergence theorem has been obtained in these cases. The results obtained here are better to some earlier results obtained by several mathematicians in the sense that (i) an artificial looking condition, used for obtaining the explicit representation of the fundamental polynomials, has been replaced by a simple interpolatory condition (ii) the results have been obtained in the case when n is considered to be odd and (iii) an improved quantitative estimate of the interpolatory polynomials has been obtained.

Biographie de l'auteur

I am presently working as an Associate Professor in the Department of Mathematics and Astronomy, University of Lucknow, India. I did my Ph.D. in 2001. My interests are in Interpolation On Real Line & Unit Circle, Chaos in Social systems, Potential Theory, Wavelets Through Trigonometric Interpolation etc.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP LAMBERT Academic Publishing
Date d'édition
2013
Langue
anglais
ISBN 10 
3845474904
ISBN 13 
9783845474908
Reliure
Broché
Nombre de pages
100
Coordonnées du fabricant
non disponible
Personne responsable
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