Spectral Theory of the Hermite Operator on Lp(Rn)
Department of Mathematics and Statistics, York
University 4700 Keele Street, Toronto, Ontario
Corresponding author. E-mail: email@example.com. This research has been supported by the Natural
Sciences and Engineering Research Council of Canada.
We prove that the minimal operator and the maximal operator of the Hermite operator are the same on Lp(ℝn) , 4 / 3 <p< 4. The domain and the spectrum of the minimal operator (=maximal operator) of the Hermite operator on Lp(ℝn), 4/3 <p< 4, are computed. In addition, we can give an estimate for the Lp-norm of the solution to the initial value problem for the heat equation governed by the minimal (maximal) operator for 4/3<p<4.
Mathematics Subject Classification: 35K05 / 47A10
Key words: Hermite operator / Hermite functions / minimal (maximal) operator / spectrum / the heat equation
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