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Spectral Theory of the Hermite Operator on Lp(Rn)

Published online by Cambridge University Press:  17 July 2014

X. Duan
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Abstract

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.

Keywords

Hermite operatorHermite functionsminimal (maximal) operatorspectrumthe heat equation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 5: Spectral problems , 2014 , pp. 39 - 43
Copyright
© EDP Sciences, 2014

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