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Book Review
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Book Information
Author(s):
Peter Kuchment
Title:
Floquet theory for partial differential equations
Additional book information:
Operator Theory Advances and Applications, vol. 60, Birkh\"auser Verlag, Basel and Boston, 1993, xiv+350 pp., US$108.50. ISBN 0-8176-2901-7
References:
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- J. E. Avron, A. Grossmann, and R. Rodriguez, Hamiltonians in the one-electron theory of solids. \rm I, Rep. Math. Phys. \textbf{5} (1974), 113--120.
- [AGR2]
- J. E. Avron, A. Grossmann, and R. Rodriguez, Spectral properties of Bloch Hamiltonians, Ann. Physics \textbf{103} (1977), 47--63.
- [B1]
- F. Bloch, \"Uber die Quantenmechanik der Elektronen in Kristallgittern, Z. Phys. \textbf{52} (1929), 555--600.
- [DK]
- Yu. L. Daletskii and M. G. Krein, Stability of solutions of differential equations in Banach space, Amer. Math. Soc., Providence, RI, 1974.
- [F1]
- G. Floquet, Sur les \'equations diff\'erentielles lin\'earies \`a coefficients p\'eriodiques, Ann. \'Ecole Norm. Sup. \textbf{12} (1883), 47--88.
- [Ge]
- I. M. Gel\cprime fand, Expansion in eigenfunctions of an equation with periodic coefficients, Dokl. Akad. Nauk SSSR \textbf{73} (1950), 1117--1120.
- [Ha]
- P. Hartman, Ordinary differential equations, Hartman, Baltimore, MD, 1973.
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- G. W. Hill, On the path of motion of the lunar perigee, Acta Math \textbf{8} (1886), 1--36 \afterall (This is a reprinting of an article which first appeared in 1877.)
- [Ho1]
- J. S. Howland, Scattering theory for Hamiltonians periodic in time, Indiana Univ. Math. J. \textbf{28} (1979), 471--494.
- [Ho2]
- J. S. Howland, Floquet operators with singular spectrum. \rm I, Ann. Inst. H. Poincar\'e \textbf{49} (1989), 309--323.
- [Ho3]
- J. S. Howland, Floquet operators with singular spectrum. \rm II, Ann. Inst. H. Poincar\'e \textbf{49} (1989), 325--334.
- [Ku]
- P. A. Kuchment, Floquet theory for partial differential equations, Russian Math. Surveys \textbf{37} (1982), 1--60.
- [Mi]
- A. I. Miloslavskii, On the Floquet theory for parabolic differential equations, Functional Anal. Appl. \textbf{10} (1976), 151--153.
- [MS]
- J. Massera and J. Sch\"affer, Differential equations and function spaces, Academic Press, New York, 1966.
- [OK]
- F. Odeh and J. B. Keller, Partial differential equations with periodic coefficients and Bloch waves in crystals, J. Math. Phys. \textbf{5} (1964), 1499--1504.
- [RS]
- M. Reed and B. Simon, Analysis of operators, Methods of Modern Mathematical Physics, vol. IV, Academic Press, New York, 1978.
- [Sk]
- M. M. Skriganov, Geometric and arithmetic methods in the spectral theory of multidimensional periodic operators, Proceedings of the Steklov Institute of Mathematics, no. 171, Amer. Math. Soc., Providence, RI, 1987.
- [Th]
- L. E. Thomas, Time dependent approach to scattering from impurities in a crystal, Comm. Math. Phys. \textbf{33} (1973), 335--343.
- [Ya]
- K. Yajima, Scattering theory for Schroedinger equation with potential periodic in time, J. Math. Soc. Japan \textbf{29} (1977), 729--743.
Additional Information:
Reviewer(s):
Evans M. Harrell
II
Review Information:
Journal:
Bull. Amer. Math. Soc.
32
(1995),
158-162.
DOI:
10.1090/S0273-0979-1995-00566-5
PII:
S 0273-0979(1995)00566-5
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