|
Divergent Laguerre series
Author(s):
Krzysztof
Stempak
Journal:
Proc. Amer. Math. Soc.
129
(2001),
1123-1126.
MSC (1991):
Primary 42C10;
Secondary 42C99
Posted:
October 16, 2000
Retrieve article in:
PDF DVI PostScript
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We prove failure of a.e. convergence of partial sums of Laguerre expansions of  functions for  . The idea which is used goes back to Stanton and Tomas. We follow Meaney's paper (1983), where divergence results were proved in the Jacobi polynomial case.
References:
-
- [Ma]
- Markett, C., Mean Cesàro summability of Laguerre expansions and norm estimates with shifted parameter, Anal. Math. 8 (1982), 19-37. MR 83j:40004
- [Me]
- Meaney, C., Divergent Jacobi polynomial series, Proc. Amer. Math. Soc. 87 (1983), 459-462. MR 84c:42040
- [M]
- Muckenhoupt, B., Equiconvergence and almost everywhere convergence of Hermite and Laguerre series, SIAM J. Math. Anal. 1 (1970), 295-321. MR 42:4948
- [Po]
- Pollard, H., The mean convergence of orthogonal series II, Trans. Amer. Math. Soc. 63 (1948), 355-367. MR 9:426e
- [St]
- Stempak, K., Transplanting maximal inequalities between Laguerre and Hankel multipliers, Monats. Math. 122 (1996), 187-197. MR 97g:42010
- [Sz]
- Szegö, G., Orthogonal Polynomials, Colloquium Publications, vol.23, American Mathematical Society, New York, 1939. MR 1:14b
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
42C10,
42C99
Retrieve articles in all Journals with MSC
(1991):
42C10,
42C99
Additional Information:
Krzysztof
Stempak
Affiliation:
Instytut Matematyczny Politechniki Wroclawskiej, Wyb. Wyspianskiego 27, 50-370 Wroclaw, Poland
Email:
stempak@im.pwr.wroc.pl
DOI:
10.1090/S0002-9939-00-05657-4
PII:
S 0002-9939(00)05657-4
Keywords:
Laguerre polynomials and functions,
divergence almost everywhere
Received by editor(s):
March 19, 1999
Received by editor(s) in revised form:
July 2, 1999
Posted:
October 16, 2000
Additional Notes:
This research was supported in part by KBN grant # 2 PO3A 048 and European Commission via the TMR network ``Harmonic Analysis'', contract no. ERB FMRX-CT970159.
Communicated by:
Christopher D. Sogge
Copyright of article:
Copyright
2000,
American Mathematical Society
|
Comments: webmaster@ams.org