In this paper we consider the sharp estimates of the growth orders of the eigenfunctions of the Schrödinger operators with potentials oscillating violently at infinity. We make use of the modified Kato's method (Comm. Pure Appl. Math., 12 (1959), 403-425) and we apply the ideas of J. Uchiyama and O. Yamada (Publ. RIMS, Kyoto Univ., 26 (1990), 419-449). Applications will be given in the next paper  in this issue.
Cite this article
Masaharu Arai, Jun Uchiyama, Growth Order of Eigenfunctions of Schrödinger Operators with Potentials Admitting Some Integral Conditions I — General Theory —. Publ. Res. Inst. Math. Sci. 32 (1996), no. 4, pp. 581–616