JournalsprimsVol. 32 , No. 4DOI 10.2977/prims/1195162714

Growth Order of Eigenfunctions of Schrödinger Operators with Potentials Admitting Some Integral Conditions II — Applications —

  • Masaharu Arai

    Nihon University, Tokyo, Japan
  • Jun Uchiyama

    Kyoto University, Japan
Growth Order of Eigenfunctions of Schrödinger Operators with Potentials Admitting Some Integral Conditions II — Applications — cover

Abstract

In this paper we give applications of M. Arai and J. Uchiyama [2, Theorems 1.1 and 1.2], which treat the sharp estimates of the growth orders of the eigenfunctions of the Schrödinger operators with potentials oscillating violently at infinity. We can generalize the results of G.B. Khosrovshahi, H.A. Levine and L.E. Payne (Trans. Amer. Math. Soc., 253 (1979), 211-228) and H. Kalf and V.K. Kumar (Trans. Amer. Math. Soc., 275 (1983), 215-229). Also we generalize the result of S. Agmon (J. Analyse Math., 23 (1970), 1-25).