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minimal (maximal) operator

Mathematical Modelling of Natural Phenomena (1)

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Spectral Theory of the Hermite Operator on Lp(Rn)
X. Duan
Journal:

Mathematical Modelling of Natural Phenomena / Volume 9 / Issue 5 / 2014

Published online by Cambridge University Press:

17 July 2014, pp. 39-43

Print publication:

2014
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We prove that the minimal operator and the maximal operator of the Hermite operator arethe same on Lp(ℝn), 4 / 3<p< 4. Thedomain and the spectrum of the minimal operator (=maximal operator) of the Hermiteoperator on Lp(ℝn),4/3 <p<4, are computed. In addition, we can give anestimate for the Lp-norm of thesolution to the initial value problem for the heat equation governed by the minimal(maximal) operator for 4/3<p<4.