New proof of Weyl's theorem

Details New proof of Weyl's theorem New proof of Weyl's theorem

2001-02-22

arxiv.org/abs/math-ph/0102030v1

Physics

Mathematical Physics

Scientific paper

Let $lu = -u^{\prime \prime} + q(x)u$, where $q(x)$ is a real-valued
$L^2_{loc}(0, \infty)$ function. H. Weyl has proved in 1910 that for any $z$,
$Imz \neq 0$, the equation $(l - z)w=0$, $x>0$, has a solution $w \in L^2(0,
\infty)$.
We prove this classical result using a new argument.

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