Estimates of Laguerre spectral projectors in Sobolev spaces.

*(English)* Zbl 0842.46017
Brezinski, Claude (ed.) et al., Orthogonal polynomials and their applications. Proceedings of the third international symposium held in Erice, Italy, June 1-8, 1990. Basel: J. C. Baltzer, IMACS Ann. Comput. Appl. Math. 9, 263-266 (1991).

Summary: Approximation by spectral methods of differential equation in unbounded domains is in general performed by Laguerre functions, i.e., Laguerre polynomials multiplied by a decaying exponential. Convergence results are derived from approximation properties of suitable projection or interpolation operators in the discrete spaces. We show convergence estimates for these operators in appropriate weighted Sobolev spaces. The weight function is chosen to obtain uniform convergence in the whole domain.

##### MSC:

46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |

65D05 | Interpolation (numerical methods) |

41A55 | Approximate quadratures |