Periodic differential operators
 Author/Creator
 Brown, B. Malcolm.
 Language
 English.
 Imprint
 Basel : Birkhäuser : Springer, 2013.
 Physical description
 viii, 216 p. ; 24 cm.
 Series
 Operator theory, advances and applications ; v. 230.
Access
Available online

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QA329.4 .B76 2013

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QA329.4 .B76 2013
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Contributors
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Floquet theory ; Introduction ; Preliminaries on ordinary differential systems ; Periodic firstorder systems ; The discriminant and stability ; Hill's equation and periodic Dirac systems ; Functional properties of Hill's discriminant ; The Mathieu equation ; Periodic, semiperiodic and twisted boundaryvalue problems
 Appendix, RofeBeketov's formula ; Chapter notes
 Oscillations. Introduction ; The Prüfer transform ; The boundaryvalue problem with separated boundary conditions ; The rotation number ; Zeros of solutions of Hill's equation ; The upper endpoints of the stability intervals ; A stepfunction 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 nonvanishing ; Chapter notes
 Spectra. Introduction ; Regular boundaryvalue problems ; The spectral function for the halfline problem ; Selfadjoint halfline operators ; The spectrum of the periodic boundaryvalue problem on the halfline ; The spectral matrix for the fullline problem ; The spectrum of the fullline 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)
Subjects
Bibliographic information
 Publication date
 2013
 Responsibility
 B. Malcolm Brown, Michael S.P. Eastham, Karl Michael Schmidt.
 Series
 Operator theory, advances and applications ; v. 230
 ISBN
 9783034805278
 3034805276