JournalsprimsVol. 32, No. 4pp. 581–616

Growth Order of Eigenfunctions of Schrödinger Operators with Potentials Admitting Some Integral Conditions I — General Theory —

  • Masaharu Arai

    Nihon University, Tokyo, Japan
  • Jun Uchiyama

    Kyoto University, Japan
Growth Order of Eigenfunctions of Schrödinger Operators with Potentials Admitting Some Integral Conditions I — General Theory — cover
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Abstract

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 [2] 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

DOI 10.2977/PRIMS/1195162713