An equiconvergence theorem for a class of eigenfunction expansions

Author:
C. G. C. Pitts

Journal:
Trans. Amer. Math. Soc. **189** (1974), 337-350

MSC:
Primary 34B25

MathSciNet review:
0330609

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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.

**[1]**Benjamin Muckenhoupt,*Equiconvergence and almost everywhere convergence of Hermite and Laguerre series*, SIAM J. Math. Anal.**1**(1970), 295–321. MR**0270055****[2]**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**0206435****[3]**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**0412544****[4]**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**0269913****[5]**C. G. C. Pitts,*On eigenfunction expansions for a positive potential function increasing slowly to infinity*, J. Differential Equations**13**(1973), 358–373. MR**0338498****[6]**Gabor Szegö,*Orthogonal polynomials*, American Mathematical Society Colloquium Publications, Vol. 23. Revised ed, American Mathematical Society, Providence, R.I., 1959. MR**0106295**

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DOI:
https://doi.org/10.1090/S0002-9947-1974-0330609-4

Article copyright:
© Copyright 1974
American Mathematical Society