Constanze Liaw, Lance Littlejohn, Jessica Stewart Kelly
Abstract:
We provide the mathematical foundation for the
-Jacobi
spectral theory.
Namely, we present a self-adjoint operator associated to the differential
expression with the exceptional
-Jacobi
orthogonal polynomials as
eigenfunctions. This proves that those polynomials are indeed eigenfunctions
of the self-adjoint operator (rather than just formal eigenfunctions).
Further, we prove the completeness of the exceptional
-Jacobi orthogonal
polynomials (of degrees
)
in the Lebesgue-Hilbert space
with the appropriate weight. In particular, the self-adjoint operator has no
other spectrum.
Submitted February 6, 2015. Published July 27, 2015.
Math Subject Classifications: 33C45, 34B24, 33C47, 34L05.
Key Words: Exceptional orthogonal polynomial; spectral theory;
self-adjoint operator; Darboux transformation.
Show me the PDF file (219 KB), TEX file, and other files for this article.
Constanze Liaw Department of Mathematics and CASPER Baylor University, One Bear Place #97328 Waco, TX 76798-7328, USA email: Constanze_Liaw@baylor.edu | |
Lance Littlejohn Department of Mathematics, Baylor University One Bear Place #97328 Waco, TX 76798-7328, USA email: Lance_Littlejohn@baylor.edu | |
Jessica Stewart Kelly Department of Mathematics Christopher Newport University 1 Avenue of the Arts Newport News, VA 23606, USA email: Jessica.Stewart@cnu.edu |
Return to the EJDE web page