Scattering at a strongly singular potential

Hubert's equation for the resolvent and the maximum principle for the equation u + V(x)u=0 is used to construct a self-adjoint extension of the operator + V(x) with a positive singular potential V(x). The properties of this operator are investigated.Translated from Matematicheskie Zametki, Vol. 8, No. 2, pp. 217–228, August, 1970.In conclusion I wish to thank sincerely A. N. Tikhonov for his interest in the work, and V. A. Il'in, V. P. Maclov, A. A. Samarskii, A. G. Sveshinkov, I. A. Shishmarev, and especially A. A. Arsen'ev for the interesting and informative discussions we had concerning this work.