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A quasi-equivalence between Borel summability and convergence for Fourier-Laguerre series at the end-point

Published online by Cambridge University Press:  20 January 2009

Lee Lorch  and
Jean Tzimbalario
Lee Lorch
Affiliation:
York University, Downsview, Ontario, Canada.
Jean Tzimbalario
Affiliation:
University of Alberta, Edmonton, Alberta, Canada.
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A suitable function f(x) 0 ≤ x < ∞, can be expanded into a Fourier series of Laguerre polynomials , whose interval of orthogonality is 0 ≤ x < ∞. The usual problems as to convergence and, lacking convergence, summability, and also the asymptotic behaviour of Lebesgue constants, arise for such developments. A summary of work on these convergence and summability problems, together with extensive references to the literature, can be found in the standard treatise by G. Szegö (5, especially Chapter IX) to whom many of these results are due.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 3 , October 1979 , pp. 217 - 226
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

REFERENCES

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