View in EDS

On the modifications of semi-classical orthogonal polynomials on nonuniform lattices.

Saved in:
Bibliographic Details
Title: On the modifications of semi-classical orthogonal polynomials on nonuniform lattices.
Authors: Mboutngam, S.1 mbsalif@gmail.com, Foupouagnigni, M.2 foupouagnigni@gmail.com, Njionou Sadjang, P.3 pnjionou@yahoo.fr
Source: Journal of Mathematical Analysis & Applications. Jan2017, Vol. 445 Issue 1, p819-836. 18p.
Subjects: Orthogonal polynomials, Lattice theory, Linear systems, Multiplication, Mathematical analysis
Abstract: Semi classical orthogonal polynomials on nonuniform lattices with respect to a linear functional L are defined as polynomials ( P n ) where the degree of P n is exactly n , the P n satisfy the orthogonality relation 〈 L , P n P m 〉 = 0 , n ≠ m , 〈 L , P n P n 〉 ≠ 0 , n ≥ 0 and L satisfies the Pearson equation D x ( ϕ L ) = S x ( ψ L ) , where ϕ is a non zero polynomial and ψ a polynomial of degree at least 1. In this work, we prove that the multiplication of semi classical linear functional by a first degree polynomial, the addition of a Dirac measure to the semi-classical regular linear functional on nonuniform lattice give semi classical linear functional but not necessary of the same class. We apply these modifications to some classical orthogonal polynomials. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 117896267
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: On the modifications of semi-classical orthogonal polynomials on nonuniform lattices.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Mboutngam%2C+S%2E%22">Mboutngam, S.</searchLink><relatesTo>1</relatesTo><i> mbsalif@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Foupouagnigni%2C+M%2E%22">Foupouagnigni, M.</searchLink><relatesTo>2</relatesTo><i> foupouagnigni@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Njionou+Sadjang%2C+P%2E%22">Njionou Sadjang, P.</searchLink><relatesTo>3</relatesTo><i> pnjionou@yahoo.fr</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Journal+of+Mathematical+Analysis+%26+Applications%22">Journal of Mathematical Analysis & Applications</searchLink>. Jan2017, Vol. 445 Issue 1, p819-836. 18p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Orthogonal+polynomials%22">Orthogonal polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Lattice+theory%22">Lattice theory</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+systems%22">Linear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Multiplication%22">Multiplication</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Semi classical orthogonal polynomials on nonuniform lattices with respect to a linear functional L are defined as polynomials ( P n ) where the degree of P n is exactly n , the P n satisfy the orthogonality relation 〈 L , P n P m 〉 = 0 , n ≠ m , 〈 L , P n P n 〉 ≠ 0 , n ≥ 0 and L satisfies the Pearson equation D x ( ϕ L ) = S x ( ψ L ) , where ϕ is a non zero polynomial and ψ a polynomial of degree at least 1. In this work, we prove that the multiplication of semi classical linear functional by a first degree polynomial, the addition of a Dirac measure to the semi-classical regular linear functional on nonuniform lattice give semi classical linear functional but not necessary of the same class. We apply these modifications to some classical orthogonal polynomials. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=117896267
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.jmaa.2016.06.041
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 18
        StartPage: 819
    Subjects:
      – SubjectFull: Orthogonal polynomials
        Type: general
      – SubjectFull: Lattice theory
        Type: general
      – SubjectFull: Linear systems
        Type: general
      – SubjectFull: Multiplication
        Type: general
      – SubjectFull: Mathematical analysis
        Type: general
    Titles:
      – TitleFull: On the modifications of semi-classical orthogonal polynomials on nonuniform lattices.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Mboutngam, S.
      – PersonEntity:
          Name:
            NameFull: Foupouagnigni, M.
      – PersonEntity:
          Name:
            NameFull: Njionou Sadjang, P.
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Text: Jan2017
              Type: published
              Y: 2017
          Identifiers:
            – Type: issn-print
              Value: 0022247X
          Numbering:
            – Type: volume
              Value: 445
            – Type: issue
              Value: 1
          Titles:
            – TitleFull: Journal of Mathematical Analysis & Applications
              Type: main
ResultId 1