Tohoku Mathematical Journal

Asymptotic distribution of eigenvalues of Schrödinger operators with nonclassical potentials

Kazuya Tachizawa

Full-text: Open access

Article information

Source
Tohoku Math. J. (2), Volume 42, Number 3 (1990), 381-406.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178227617

Digital Object Identifier
doi:10.2748/tmj/1178227617

Mathematical Reviews number (MathSciNet)
MR1066668

Zentralblatt MATH identifier
0726.35091

Subjects
Primary: 35P20: Asymptotic distribution of eigenvalues and eigenfunctions
Secondary: 35J10: Schrödinger operator [See also 35Pxx] 47F05: Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47)

Citation

Tachizawa, Kazuya. Asymptotic distribution of eigenvalues of Schrödinger operators with nonclassical potentials. Tohoku Math. J. (2) 42 (1990), no. 3, 381--406. doi:10.2748/tmj/1178227617. https://projecteuclid.org/euclid.tmj/1178227617


Export citation

References

  • [1] R. R. COIFMAN AND C. FEFFERMAN, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241-250.
  • [2] D. E. EDMUNDS AND W. D. EVANS, On the distribution of eigenvalues of Schrdinger operators, Arch Rational Mech. Anal. 89 (1985), 135-167.
  • [3] C. FEFFERMAN, Theuncertaintyprinciple, Bull. Amer. Math. Soc. 9 (1983), 129-206
  • [4] J. GARCIA-CUERVA AND J. L. RUBIO DEFRANCIA, Weighted norm inequalities and related topics, North-Holland, Amsterdam, 1985.
  • [5] T. KATO, Schrdinger operators with singular potentials, Israel J. Math. 13(1972), 135-148
  • [6] Y. MORIMOTO, The uncertainty principle and hypoelliptic operators, Publ. Res. Inst. Math. Sci. 2 (1987), 955-964.
  • [7] M. REED AND B. SIMON, Method of modern mathematical physics, vol. IV, Academic Press, Ne York, 1978.
  • [8] D. ROBERT, Comportement asymptotique des valeurs propres d'operateurs du type Schrdinger potential «degenere», J. Math. Pures Appl. 61 (1982), 275-300.
  • [9] G. V. ROZENBLJUM, Asymptotics of theeigenvalues of the Schrdinger operator, Math. USSR-Sb. 2 (1974), 349-371.
  • [10] B. SIMON, Nonclassical eigenvalue asymptotics, J. Funct. Anal. 53 (1983), 84-98
  • [11] B. SIMON, Some quantum operators with discrete spectrum but classically continuous spectrum, Ann Physics. 146 (1983), 209-220.
  • [12] M. Z. SOLOMYAK, Asymptotics of the spectrum of the Schrdinger operator with nonregula homogeneous potential, Math. USSR-Sb. 55 (1986), 19-37.