The Energy Space of Hermite Operator in R^n and Associated Sobolev Spaces
published by Tishreen University
in 2014
in Mathematics
and research's language is
العربية
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Abstract in English
In this paper we study the energy space of the Hermite differential operator
and prove that it is a Hilbert space with a suitable inner product. Then we construct the powers of , denoted by , by using the spectral theory . We will see that has similar properties as for real numbers s > o, therefore we can construct new Hilbert spaces which are the energy spaces of powers of . They are Sobolev spaces.
References used
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BONJIOANNI, B.;ROGERS, K.M . Regularity of the Schrödinger equation for the Harmonic oscillator.2008