An equiconvergence theorem for a class of eigenfunction expansions

Pitts, C. G. C.

doi:10.1090/S0002-9947-1974-0330609-4

An equiconvergence theorem for a class of eigenfunction expansions
HTML articles powered by AMS MathViewer

by C. G. C. Pitts PDF

Trans. Amer. Math. Soc. 189 (1974), 337-350 Request permission

Abstract:

A recent result of Muckenhoupt concerning the convergence of the expansion of an arbitrary function in terms of the Hermite series of orthogonal polynomials is generalised to a class of orthogonal expansions which arise from an eigenfunction problem associated with a second-order linear differential equation.

References

Benjamin Muckenhoupt, Equiconvergence and almost everywhere convergence of Hermite and Laguerre series, SIAM J. Math. Anal. 1 (1970), 295–321. MR 270055, DOI 10.1137/0501027
C. G. C. Pitts, Simplified asymptotic approximations to solutions of a second-order differential equation, Quart. J. Math. Oxford Ser. (2) 17 (1966), 307–320. MR 206435, DOI 10.1093/qmath/17.1.307
C. G. C. Pitts, Simplified asymptotic approximations to solutions of a second-order differential equation, Quart. J. Math. Oxford Ser. (2) 21 (1970), 223–242. MR 412544, DOI 10.1093/qmath/21.2.223
C. G. C. Pitts, An equiconvergence result of eigenfunction expansions for a positive increasing potential function, Quart. J. Math. Oxford Ser. (2) 21 (1970), 357–369. MR 269913, DOI 10.1093/qmath/21.3.357
C. G. C. Pitts, On eigenfunction expansions for a positive potential function increasing slowly to infinity, J. Differential Equations 13 (1973), 358–373. MR 338498, DOI 10.1016/0022-0396(73)90022-3
Gabor Szegö, Orthogonal polynomials, American Mathematical Society Colloquium Publications, Vol. 23, American Mathematical Society, Providence, R.I., 1959. Revised ed. MR 0106295