Cwikel's theorem and the CLR inequality

  • Rupert L. Frank

    Caltech, Pasadena, United States


We give a short proof of the CLR bound on the number of negative eigenvalues of Schrödinger operators. The argument, which is based on work of Rumin, leads to remarkably good constants and applies to the case of operator-valued potentials as well. Moreover, we obtain the general form of Cwikel's estimate about the singular values of operators of the form f(X)g(i)f(X) g(-i\nabla).

Cite this article

Rupert L. Frank, Cwikel's theorem and the CLR inequality. J. Spectr. Theory 4 (2014), no. 1, pp. 1–21

DOI 10.4171/JST/59