$L^\infty$-Uniqueness of Generalized SCHRÖdinger Operators

Details $L^\infty$-Uniqueness of Generalized SCHRÖdinger Operators $L^\infty$-Uniqueness of Generalized SCHRÖdinger Operators

2008-01-17

arxiv.org/abs/0801.2755v1

Physics

Mathematical Physics

Scientific paper

The main purpose of this paper is to show that the generalized Schr\"odinger
operator ${\cal A}^Vf={1/2}\Delta f+b\nabla f-Vf$, $f\in C_0^\infty(\R^d)$, is
a pre-generator for which we can prove its $L^\infty(\R^d,dx)$-uniqueness.
Moreover, we prove the $L^1(\R^d,dx)$-uniqueness of weak solutions for the
Fokker-Planck equation associated with this pre-generator.

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