On the genericity of nonvanishing instability intervals in Hills equation

Barry Simon

Annales de l'I.H.P. Physique théorique (1976)

  • Volume: 24, Issue: 1, page 91-93
  • ISSN: 0246-0211

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Simon, Barry. "On the genericity of nonvanishing instability intervals in Hills equation." Annales de l'I.H.P. Physique théorique 24.1 (1976): 91-93. <http://eudml.org/doc/75888>.

@article{Simon1976,
author = {Simon, Barry},
journal = {Annales de l'I.H.P. Physique théorique},
language = {eng},
number = {1},
pages = {91-93},
publisher = {Gauthier-Villars},
title = {On the genericity of nonvanishing instability intervals in Hills equation},
url = {http://eudml.org/doc/75888},
volume = {24},
year = {1976},
}

TY - JOUR
AU - Simon, Barry
TI - On the genericity of nonvanishing instability intervals in Hills equation
JO - Annales de l'I.H.P. Physique théorique
PY - 1976
PB - Gauthier-Villars
VL - 24
IS - 1
SP - 91
EP - 93
LA - eng
UR - http://eudml.org/doc/75888
ER -

References

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  1. [1] G. Borg, Eine umkehrung der Sturm-Liouvillschen eigenwertaufgabe. Bestimmung der differentialgleichung durch die eigenwert. Acta Math., t. 78, 1946, p. 1-96. Zbl0063.00523MR15185
  2. [2] G. Choquet, Lectures in Analysis, Vol. I. Benjamin, New York, 1969. Zbl0181.39601
  3. [3] M.S.P. Eastham, The Spectral Theory of Periodic Differential Equations. Scottish Academic Press, 1973. Zbl0287.34016
  4. [4] W. Goldberg, On the determination of a Hills equation from its spectrum. Bull. A. M. S., t. 80, 1974, p. 1111-1112. Zbl0303.34022MR364726
  5. [5] H. Hochstadt, On the determination of a Hill's equation from its spectrum, I. Arch. Rat. Mach. Ancl., t. 19, 1965, p. 353-362. Zbl0128.31201MR181792
  6. [6] H. Hochstadt, On the determination of a Hills equation from its spectrum, II. Arch. Rat. Mach. Ancl., t. 23, 1966, p. 237-238. Zbl0146.31905MR200520
  7. [7] E.L. Ince, A proof of the impossibility of the coexistence of two Mathieu functions. Proc. Comb. Phil., Vol. 21, 1922, p. 117-120. Zbl48.1263.02JFM48.1263.02
  8. [8] T. Kato, Perturbation theory of linear operators. Springer, 1966. Zbl0148.12601
  9. [9] W. Magnus and S. Winkler, Hill's Equation. Interscience, 1966. Zbl0158.09604
  10. [10] M. Reed and B. Simon, Methods of Modern Mathematical Physics, III.Analysis of Operators. Academic Press, expected 1976. Zbl0405.47007
  11. [11] F. Rellich, Storungs theory der Spektalzerlegung, I-V. Math. Ann., t. 113, 1937, p. 600-619 ; t. 113, 1937, p. 677-685 ; t. 116, 1939, p. 555-560 ; t. 117, 1940, p. 356- 382 ; t. 118, 1942, p. 462-484. 

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