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Periodic differential operators / B. Malcolm Brown, Michael S.P. Eastham, Karl Michael Schmidt.

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Author/Creator:
Brown, B. Malcolm.
Language:
English.
Publication date:
2013
Imprint:
Basel : Birkhäuser : Springer, 2013.
Format:
  • Book
  • viii, 216 p. ; 24 cm.
Bibliography:
Includes bibliographical references and index.
Contents:
  • Floquet theory ; Introduction ; Preliminaries on ordinary differential systems ; Periodic first-order systems ; The discriminant and stability ; Hill's equation and periodic Dirac systems ; Functional properties of Hill's discriminant ; The Mathieu equation ; Periodic, semi-periodic and twisted boundary-value problems
  • Appendix, Rofe-Beketov's formula ; Chapter notes
  • Oscillations. Introduction ; The Prüfer transform ; The boundary-value problem with separated boundary conditions ; The rotation number ; Zeros of solutions of Hill's equation ; The upper end-points of the stability intervals ; A step-function example ; Even coefficients ; Comparison of eigenvalues ; Least eigenvalues ; Chapter notes
  • Asymptotics. Introduction ; Prüfer transformation formulae ; The coefficient w ; Titchmarsh's asymptotic formula ; Differentiable q ; Length of the instability intervals ; The Mathieu equation ; Asymptotic formulae for solutions ; Absence of instability intervals ; Absence of all but N finite instability intervals ; Absence of odd instability intervals ; All instability intervals non-vanishing ; Chapter notes
  • Spectra. Introduction ; Regular boundary-value problems ; The spectral function for the half-line problem ; Self-adjoint half-line operators ; The spectrum of the periodic boundary-value problem on the half-line ; The spectral matrix for the full-line problem ; The spectrum of the full-line periodic problem ; Oscillations and spectra ; Bounded solutions and the absolutely continuous spectrum ; Chapter notes
  • Perturbations. Introduction ; Spectral bands ; Gap eigenvalues ; Critical coupling constants ; Eigenvalue asymptotics ; Chapter notes.
Contributor:
Eastham, M. S. P. (Michael Stephen Patrick)
Schmidt, Karl Michael.
Series:
Operator theory, advances and applications ; v. 230.
Subjects:
ISBN:
9783034805278
3034805276

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