Left-definite theory with applications to orthogonal polynomials
| Autor: | Andrea Bruder, Davut Tuncer, Lance L. Littlejohn, R. Wellman |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Self-adjoint operator
Jacobi–Stirling numbers Hermite polynomials Differential equation Applied Mathematics Hilbert space Sobolev space Stirling numbers of the second kind Algebra Classical orthogonal polynomials Computational Mathematics symbols.namesake Left-definite Hilbert space Orthogonal polynomials Laguerre polynomials symbols Legendre–Stirling numbers Dirichlet inner product Left-definite self-adjoint operator Mathematics |
| Zdroj: | Journal of Computational and Applied Mathematics. 233:1380-1398 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2009.02.058 |
| Popis: | In the past several years, there has been considerable progress made on a general left-definite theory associated with a self-adjoint operator A that is bounded below in a Hilbert space H; the term ‘left-definite’ has its origins in differential equations but Littlejohn and Wellman [L. L. Littlejohn, R. Wellman, A general left-definite theory for certain self-adjoint operators with applications to differential equations, J. Differential Equations, 181 (2) (2002) 280–339] generalized the main ideas to a general abstract setting. In particular, it is known that such an operator A generates a continuum {Hr}r>0 of Hilbert spaces and a continuum of {Ar}r>0 of self-adjoint operators. In this paper, we review the main theoretical results in [L. L. Littlejohn, R. Wellman, A general left-definite theory for certain self-adjoint operators with applications to differential equations, J. Differential Equations, 181 (2) (2002) 280–339]; moreover, we apply these results to several specific examples, including the classical orthogonal polynomials of Laguerre, Hermite, and Jacobi. |
| Databáze: | OpenAIRE |
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