@article{AIHPA_1989__51_1_45_0, author = {Benettin, Giancarlo and Chierchia, Luigi and Fass\`o, Francesco}, title = {Exponential estimates on the one-dimensional {Schroedinger} equation with bounded analytic potential}, journal = {Annales de l'I.H.P. Physique th\'eorique}, pages = {45--66}, publisher = {Gauthier-Villars}, volume = {51}, number = {1}, year = {1989}, mrnumber = {1029849}, zbl = {0713.34054}, language = {en}, url = {http://www.numdam.org/item/AIHPA_1989__51_1_45_0/} }
TY - JOUR AU - Benettin, Giancarlo AU - Chierchia, Luigi AU - Fassò, Francesco TI - Exponential estimates on the one-dimensional Schroedinger equation with bounded analytic potential JO - Annales de l'I.H.P. Physique théorique PY - 1989 SP - 45 EP - 66 VL - 51 IS - 1 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1989__51_1_45_0/ LA - en ID - AIHPA_1989__51_1_45_0 ER -
%0 Journal Article %A Benettin, Giancarlo %A Chierchia, Luigi %A Fassò, Francesco %T Exponential estimates on the one-dimensional Schroedinger equation with bounded analytic potential %J Annales de l'I.H.P. Physique théorique %D 1989 %P 45-66 %V 51 %N 1 %I Gauthier-Villars %U http://www.numdam.org/item/AIHPA_1989__51_1_45_0/ %G en %F AIHPA_1989__51_1_45_0
Benettin, Giancarlo; Chierchia, Luigi; Fassò, Francesco. Exponential estimates on the one-dimensional Schroedinger equation with bounded analytic potential. Annales de l'I.H.P. Physique théorique, Tome 51 (1989) no. 1, pp. 45-66. http://www.numdam.org/item/AIHPA_1989__51_1_45_0/
[1] Hill's Equation, Wiley and Sons, New York, 1966. | MR | Zbl
and ,[2] Commun. Pure Appl. Math., Vol. 30, 1977, pp. 321-337. | MR | Zbl
,[3] 29, 1983, pp. 211-338. | Numdam | MR | Zbl
, Ann. Inst. Henri-Poincaré, Vol.[4] Ann. Scient. Ec. Norm. Sup., 4e serie, Vol. 20, 1987, pp. 641-672. | Numdam | MR | Zbl
,[5] Usp. Mat. Nauk, Vol. 32, 1977 [Russ. Math. Surv., Vol. 32, 1, 1977].
,[6] Trudy Sem. Petrows., No. 5, 1979, p. 5 [Topics in Modern Mathematics, Petrovskii Sem. No. 5, O.A. Oleinik editor (Consultant Bureau, New York, 1985)]. | MR
,[7] Quasi-Integrable Mechanical Systems, in Critical phenomena, Random Systems, Gauge Theories, K. OSTERWALDER and R. STORA Eds., Les Houches, Session XLIII, 1984 (North-Holland, Amsterdam, 1986). | MR | Zbl
,[8] Prikl. Matem. Mekan., Vol. 45, 1981, p. 80 (PMM U.S.S.R., Vol. 45, 1982, p. 58). | MR | Zbl
,[9] Celestial Mechanics, Vol. 37, 1985, p. 95. | MR
and ,[10] J. Stat. Phys., Vol. 44, 1985, p. 293. | MR | Zbl
and ,[11] J. Stat. Phys., Vol. 45, 1986, pp. 41-47; Vol. 49, 1987, pp. 829-840. | Zbl
and :[12] Comm. Math. Phys., Vol. 113, 1987, p. 87. | MR | Zbl
, and ,[13] Comm. Math. Phys., Vol. 121, 1989, p. 557. | MR | Zbl
, and ,[14] Differentsial'nye Uravneniya, Vol. 12, 1976, pp. 1012-1018 (Diff. Eq., Vol. 12, 1976, pp. 713-718). | MR
,[15] Functional Anal. Appl., Vol. 9, 1975, pp. 279-289. | Zbl
and ,[16] Ann. N. Y. Acad. Sci., Vol. 357, 1980, pp. 90-107. | MR | Zbl
,[17] Comment. Math. Helvetici, Vol. 59, 1984, pp. 39-85. | MR | Zbl
and ,[18] J. Math. Phys., Vol. 28, 1987, pp. 2891-2898. | Zbl
,[19] Methods of modern mathematical phisics, Vol. 3: Scattering theory, Academic Press, New York, 1979. | MR | Zbl
and ,[20] On Optimal Estimates for the Solutions of Linear Partial Differential Equations of first Order with Constant Coefficients on the Torus, in Dynamical Systems, Theory and Applications, J. MOSER Ed., Lect. Notes Phys., No. 38, Springer-Verlag, Berlin, 1975. | MR | Zbl
,[21] Comm. Pure Appl. Math., Vol. 29, 1976, p. 755. | MR
,[22] J. Funct. Anal., Vol. 42, 1981, pp. 347-355. | MR | Zbl
,[23] Ann. Phys. (N.Y.), Vol. 134, 1980, pp. 76-84. | MR | Zbl
and ,[24] Localization for a class of one-dimensional quasi-periodic Schroedinger operators, to appear in Comm. Math. Phys. | Zbl
, and ,