Skip to main content Accessibility help

Bloch waves and multiparameter spectral theory

  • B. P. Rynne (a1) and B. D. Sleeman (a1)


We study the spectral theory of a multiparameter system of periodic Schrödinger operators. Bloch waves are generalized eigenfunctions of these operators and are used to give eigenfunction expansion theorems and to derive some properties of the spectrum of the system.



Hide All
1Binding, P.. Left definite multiparameter eigenvalue problems. Trans. Amer. Math. Soc. 272 (1982), 475486.
2Cartan, H.. Variétés analytiques-réelles et variété analytiques-complexes. Bull. Soc. Math. France 85 (1957), 77100.
3Cracknell, A. P. and Wong, K. C.. The Fermi Surface (Oxford: Clarendon Press, 1973).
4Dieudonné, J.. Foundations of Modern Analysis (London: Academic Press, 1969).
5Dunford, N. and Schwartz, J. T.. Linear Operators I (New York: Interscience, 1958).
6Eastham, M. S. P.. The Spectral Theory of Periodic Differential Equations (Edinburgh: Scottish Academic Press, 1973).
7Kato, T.. Perturbation Theory for Linear Operators (New York: Springer-Verlag, 1976).
8Lions, J. L. and , E. Magenes. Non-homogeneous Boundary Value Problems and Applications I (New York: Springer, 1972).
9Odeh, F. and Keller, J. B.. Partial differential equations with periodic coefficients and Bloch waves in crystals. J. Math. Phys. 5 (1964), 14991504.
10Sleeman, B. D.. Multiparameter Spectral Theory in Hilbert space (London: Pitman, 1978).
11Smithies, F.. Integral Equations (London: Cambridge University Press, 1958).
12Whitney, H.. Complex Analytic Varieties (Reading, Mass.: Addison Wesley, 1972).
13Wilcox, C. H.. Theory of Bloch waves. J. Analyse Math. 33 (1978), 146167.
14Wilcox, C. H.. Measurable eigenvectors for Hermitian matrix-valued polynomials. J. Math, Anal. Appl. 40 (1972), 1219.
15Ziman, J. M., Principles of the Theory of Solids (Cambridge University Press, 1972).


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed