Back to Search
Start Over
Asymptotically extremal polynomials with respect to varying weights and application to Sobolev orthogonality
- Source :
-
Journal of Mathematical Analysis & Applications . Oct2008, Vol. 346 Issue 2, p480-488. 9p. - Publication Year :
- 2008
-
Abstract
- Abstract: We study the asymptotic behavior of the zeros of a sequence of polynomials whose weighted norms, with respect to a sequence of weight functions, have the same nth root asymptotic behavior as the weighted norms of certain extremal polynomials. This result is applied to obtain the (contracted) weak zero distribution for orthogonal polynomials with respect to a Sobolev inner product with exponential weights of the form , giving a unified treatment for the so-called Freud (i.e., when φ has polynomial growth at infinity) and Erdös (when φ grows faster than any polynomial at infinity) cases. In addition, we provide a new proof for the bound of the distance of the zeros to the convex hull of the support for these Sobolev orthogonal polynomials. [Copyright &y& Elsevier]
- Subjects :
- *POLYNOMIALS
*SOBOLEV spaces
*ORTHOGONAL functions
*MATHEMATICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 346
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 32738619
- Full Text :
- https://doi.org/10.1016/j.jmaa.2008.05.029