Spectral Theory of X1-Laguerre Polynomials
نویسندگان
چکیده
In 2009, Gómez–Ullate, Kamran, and Milson characterized all sequences of polynomials {pn}n=1, with deg pn = n ≥ 1, that are eigenfunctions of a second– order differential equation and are orthogonal with respect to a positive Borel measure on the real line having finite moments of all orders. Up to a complex linear change of variable, the only such sequences are the X1-Laguerre and the X1-Jacobi polynomials. In this paper, we discuss the self-adjoint operator, generated by the second-order X1-Laguerre differential expression, that has the X1-Laguerre polynomials as eigenfunctions. AMS Subject Classifications: 33C65, 34B20, 47B25.
منابع مشابه
The Spectral Theory of the X1-Laguerre Polynomials
In 2009, Gómez-Ullate, Kamran, and Milson characterized all sequences of polynomials {pn}n=1, with deg pn = n ≥ 1, that are eigenfunctions of a secondorder differential equation and are orthogonal with respect to a positive Borel measure on the real line having finite moments of all orders. Up to a complex linear change of variable, the only such sequences are theX1-Laguerre and theX1-Jacobi po...
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