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Periodic Differential Operators

  • Book
  • © 2013

Overview

Authors:
  1. B. Malcolm Brown

    1. Cardiff School of Computer Science, and Informatics, Cardiff University, Cardiff, United Kingdom

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  2. Michael S.P. Eastham

    1. Cardiff School of, Computer Science, Cardiff University, Cardiff, United Kingdom

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  3. Karl Michael Schmidt

    1. , School of Mathematics, Cardiff University, Cardiff, United Kingdom

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  • Comprehensive treatment of one-dimensional periodic systems from the differential equation, boundary-value problem and operator-theoretic points of view
  • Unified analysis of periodic Sturm-Liouville- and Dirac-type operators by the use of oscillation methods
  • Study of perturbed periodic problems
  • Includes supplementary material: sn.pub/extras

Part of the book series: Operator Theory: Advances and Applications (OT, volume 228)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-viii
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  2. Floquet Theory

    • B. Malcolm Brown, Michael S. P. Eastham, Karl Michael Schmidt
    Pages 1-29

  3. Oscillations

    • B. Malcolm Brown, Michael S. P. Eastham, Karl Michael Schmidt
    Pages 31-65

  4. Asymptotics

    • B. Malcolm Brown, Michael S. P. Eastham, Karl Michael Schmidt
    Pages 67-111

  5. Spectra

    • B. Malcolm Brown, Michael S. P. Eastham, Karl Michael Schmidt
    Pages 113-159

  6. Perturbations

    • B. Malcolm Brown, Michael S. P. Eastham, Karl Michael Schmidt
    Pages 161-195

  7. Back Matter

    Pages 197-216
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Keywords

About this book

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.

Reviews

From the reviews:

“It consists of five chapters, and all chapters close with a great number of additional explanatory notes connecting the results with a thorough bibliography. … It contains a rich list of 210 references of carefully selected old and new works, which, also, might be a good source to graduates for further study of the theory of periodic differential operators.” (George Karakostas, zbMATH, Vol. 1267, 2013)

Authors and Affiliations

  • Cardiff School of Computer Science, and Informatics, Cardiff University, Cardiff, United Kingdom

    B. Malcolm Brown

  • Cardiff School of, Computer Science, Cardiff University, Cardiff, United Kingdom

    Michael S.P. Eastham

  • , School of Mathematics, Cardiff University, Cardiff, United Kingdom

    Karl Michael Schmidt

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