95-189 Timo Weidl
On the Lieb-Thirring constants L_gamma,1 for gamma geq 1/2. (31K, AMS-LATEX) Apr 5, 95
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Abstract. Let $E_i(H)$ denote the negative eigenvalues of the one-dimensional Schr\"odinger operator $Hu:=-u^{\prime\prime}-Vu,\ V\geq 0,$ on $L_2({\Bbb R}).$ We prove the inequality % $$\label{1} \sum_i|E_i(H)|^\gamma\leq L_{\gamma,1}\int_{\Bbb R} V^{\gamma+1/2}(x)dx,$$ % for the "limit" case $\gamma=1/2.$ This will imply improved estimates for the best constants $L_{\gamma,1}$ in \eqref{1} as \$1/2<\gamma<3/2.

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