Periodic differential operators
QA329.4 .B76 2013
- Unknown QA329.4 .B76 2013
- Includes bibliographical references and index.
- 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.
- Publisher's Summary
- Periodic differential operators have a rich mathematical theory as well as important physical applications. They have been the subject of intensive development for over a century and remain a fertile research area. This book lays out the theoretical foundations and then moves on to give a coherent account of more recent results, relating in particular to the eigenvalue and spectral theory of the Hill and Dirac equations. The book will be valuable to advanced students and academics both for general reference and as an introduction to active research topics.
(source: Nielsen Book Data)
- Publication date
- B. Malcolm Brown, Michael S.P. Eastham, Karl Michael Schmidt.
- Operator theory, advances and applications ; v. 230