Quasi-definiteness of generalized Uvarov transforms of moment functionals
Kim, D. H. ; Kwon, K. H.
J. Appl. Math., Tome 1 (2001) no. 2, p. 69-90 / Harvested from Project Euclid
When $\sigma$ is a quasi-definite moment functional with the monic orthogonal polynomial system $\{P_{n}(x)\}_{n=0}^{\infty}$ , we consider a point masses perturbation $\tau$ of $\sigma$ given by $\tau :=\sigma +\lambda \sum_{l=1}^{m}\sum_{k=0}^{m_{l}}({(-1)^{k}u_{lk}}/{k!})\delta^{(k)}(x-c_{l})$ , where $\lambda,u_{lk}$ , and $c_l$ are constants with $c_i\neq c_j$ for $i\neq j$ . That is, $\tau$ is a generalized Uvarov transform of $\sigma$ satisfying $A(x)\tau = A(x)\sigma$ , where $A(x) =\prod_{l=1}^{m}(x-c_{l})^{m_{l}+1}$ . We find necessary and sufficient conditions for $\tau$ to be quasi-definite. We also discuss various properties of monic orthogonal polynomial system $\{R_{n}(x)\}_{n=0}^{\infty}$ relative to $\tau$ including two examples.
Publié le : 2001-05-14
Classification:  33C45
@article{1047575698,
     author = {Kim, D. H. and Kwon, K. H.},
     title = {Quasi-definiteness of generalized Uvarov transforms of moment functionals},
     journal = {J. Appl. Math.},
     volume = {1},
     number = {2},
     year = {2001},
     pages = { 69-90},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1047575698}
}
Kim, D. H.; Kwon, K. H. Quasi-definiteness of generalized Uvarov transforms of moment functionals. J. Appl. Math., Tome 1 (2001) no. 2, pp.  69-90. http://gdmltest.u-ga.fr/item/1047575698/