Applications of weighted Laguerre transplantation theorems
Authors: George Gasper and Walter Trebels
Dedicated to Dick Askey on the occasion of his 65th birthday
Abstract:
As applications of the weighted transplantation theorems in
Stempak and Trebels [On weighted transplantation and multipliers for
Laguerre expansions, Math. Ann., 300 (1994), 203 - 219.]
we consider (i) the characterization of one-dimensional Hermite
multipliers via Laguerre multipliers, (ii) extension theorems
for Laguerre multipliers in the spirit of Theorem 6.5 in
Coifman and Weiss [Transference Methods is Analysis, CBMS No. 31,
Amer. Math. Soc., Providence, R.I., 1977.],
and (iii)
necessary conditions for Laguerre multipliers via backward differences.
Key words. Laguerre and Hermite multipliers, extension theorems, backward differences
AMS(MOS) subject classifications.
Primary: 33C45, 42A45, 42C10; Secondary: 39A70
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