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Theory of Bloch waves

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References

  1. S. Agmon,Lectures on Elliptic Boundary Value Problems, Van Nostrand, New York, 1965.

    MATH  Google Scholar 

  2. F. Bloch,Über die Quantenmechanik der Electronen in Kristallgittern, Z. Phys.52 (1928), 555–600.

    Google Scholar 

  3. S. Bochner and W. T. Martin,Several Complex Variables, Princeton Univ. Press, Princeton, 1948.

    MATH  Google Scholar 

  4. T. Carleman,Zur Theorie der linearen Integralgleichungen, Math. Z.9 (1921), 196–217.

    Article  MathSciNet  Google Scholar 

  5. H. Cartan,Variétés analytiques-réelles et variétés analytiques-complexes, Bull. Soc. Math. France85 (1957), 77–100.

    MATH  MathSciNet  Google Scholar 

  6. A. P. Cracknell and K. C. Wong,The Fermi Surface, Clarendon Press, Oxford, 1973.

    Google Scholar 

  7. M. S. P. Eastham,The Schrödinger equation with a periodic potential, Proc. Roy. Soc. Edinburgh69A (1971), 125–131.

    MathSciNet  Google Scholar 

  8. M. S. P. Eastham,The Spectral Theory of Periodic Differential Equations, Scottish Academic Press, Edinburgh, 1973.

    MATH  Google Scholar 

  9. I. M. Gelfand,Expansion in series of eigenfunctions of an equation with periodic coefficients, Dokl. Akad. Nauk SSSR73 (1950), 1117–1120.

    Google Scholar 

  10. E. Goursat,A Course in Mathematical Analysis, V. III Part 2, Dover Publications, Inc., New York, 1964.

    Google Scholar 

  11. E. Hille and R. S. Phillips,Functional Analysis and Semi-groups, AMS Colloquium Publications V. 31, Providence, 1957.

  12. T. Kato,Perturbation Theory for Linear Operators, Springer, New York, 1966.

    MATH  Google Scholar 

  13. J. L. Lions and E. Magenes,Non-Homogeneous Boundary Value Problems and Applications I, Springer, New York, 1972.

    MATH  Google Scholar 

  14. S. G. Mikhlin,Integral Equations, 2nd revised ed., Pergamon Press, Oxford, 1964.

    MATH  Google Scholar 

  15. F. Odeh and J. B. Keller,Partial differential equations with periodic coefficients and Bloch waves in crystals, J. Math. Phys.5 (1964), 1499–1504.

    Article  MATH  MathSciNet  Google Scholar 

  16. F. Rellich,Ein Satz über mittlere Konvergenz, Gött. Nachr. (math. phys.) (1930), 30–35.

  17. R. Sikorski,The determinant theory in Banach spaces, Colloq. Math.8 (1961), 141–198.

    MATH  MathSciNet  Google Scholar 

  18. R. Sikorski,On the Carleman determinants, Studia Math.20 (1961), 327–346.

    MATH  MathSciNet  Google Scholar 

  19. F. Smithies,The Fredholm theory of integral equations, Duke Math. J.8 (1941), 107–130.

    Article  MATH  MathSciNet  Google Scholar 

  20. L. E. Thomas,Time dependent approach to scattering from impurities in a crystal, Comm. Math. Phys.33 (1973), 335–343.

    Article  MathSciNet  Google Scholar 

  21. E. C. Titchmarsh,Eigenfunction Expansions Part II, Clarendon Press, Oxford, 1958.

    Google Scholar 

  22. H. Whitney,Elementary structure of real algebraic varieties. Ann. of Math.66 (1957), 545–556.

    Article  MathSciNet  Google Scholar 

  23. H. Whitney and F. Bruhat,Quelques propriétés fondamentales des ensembles analytiques-réels, Comm. Math. Helvetici33 (1959), 132–160.

    Article  MathSciNet  Google Scholar 

  24. C. H. Wilcox,Uniform asymptotic estimates for wave packets in the quantum theory of scattering, J. Math. Phys.6 (1965), 611–620.

    Article  MATH  MathSciNet  Google Scholar 

  25. C. H. Wilcox,Measurable eigenvectors for Hermitian matrix-valued polynomials, J. Math. Anal. Appl.40 (1972), 12–19.

    Article  MATH  MathSciNet  Google Scholar 

  26. J. M. Ziman,Principles of the Theory of Solids, 2nd ed., Cambridge Univ. Press, 1972.

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This research was supported by the Office of Naval Research and by the Alexander von Humboldt Foundation.

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Wilcox, C.H. Theory of Bloch waves. J. Anal. Math. 33, 146–167 (1978). https://doi.org/10.1007/BF02790171

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  • DOI: https://doi.org/10.1007/BF02790171

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