|
Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
Retrieve article in:
PDF
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:
-
- [AGR1]
- J. E. Avron, A. Grossmann, and R. Rodriguez, Hamiltonians in the one-electron theory of solids. I, Rep. Math. Phys. 5 (1974), 113-120. MR 0413859 (54:1971)
- [AGR2]
- -, Spectral properties of Bloch Hamiltonians, Ann. Physics 103 (1977), 47-63. MR 0428990 (55:2010)
- [B1]
- F. Bloch, Über die Quantenmechanik der Elektronen in Kristallgittern, Z. Phys. 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. MR 0352639 (50:5126)
- [F1]
- G. Floquet, Sur les équations différentielles linéarles à coefficients périodiques, Ann. École Norm. Sup. 12 (1883), 47-88. MR 1508722
- [Ge]
- I. M. Gel'fand, Expansion in eigenfunctions of an equation with periodic coefficients, Dokl. Akad. Nauk SSSR 73 (1950), 1117-1120. MR 0039154 (12:503a)
- [Ha]
- P. Hartman, Ordinary differential equations, Hartman, Baltimore, MD, 1973. MR 0344555 (49:9294)
- [Hi]
- G. W. Hill, On the path of motion of the lunar perigee, Acta Math 8 (1886), 1-36. (This is a reprinting of an article which first appeared in 1877.) MR 1554690
- [Ho1]
- J. S. Howland, Scattering theory for Hamiltonians periodic in time, Indiana Univ. Math. J. 28 (1979), 471-494. MR 529679 (80e:47008)
- [Ho2]
- -, Floquet operators with singular spectrum. I, Ann. Inst. H. Poincaré 49 (1989), 309-323.
- [Ho3]
- -, Floquet operators with singular spectrum. II, Ann. Inst. H. Poincaré 49 (1989), 325-334.
- [Ku]
- P. A. Kuchment, Floquet theory for partial differential equations, Russian Math. Surveys 37 (1982), 1-60. MR 667973 (84b:35018)
- [Mi]
- A. I. Miloslavskii, On the Floquet theory for parabolic differential equations, Functional Anal. Appl. 10 (1976), 151-153. MR 0473390 (57:13057)
- [MS]
- J. Massera and J. Schäffer, 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. 5 (1964), 1499-1504. MR 0168924 (29:6180)
- [RS]
- M. Reed and B. Simon, Analysis of operators, Methods of Modern Mathematical Physics, vol. IV, Academic Press, New York, 1978. MR 0493421 (58:12429c)
- [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. MR 798454 (87h:47110)
- [Th]
- L. E. Thomas, Time dependent approach to scattering from impurities in a crystal, Comm. Math. Phys. 33 (1973), 335-343. MR 0334766 (48:13084)
- [Ya]
- K. Yajima, Scattering theory for Schroedinger equation with potential periodic in time, J. Math. Soc. Japan 29 (1977), 729-743. MR 0470525 (57:10276)
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
|