Phase space tunneling for operators with symbols in a Gevrey class

Journal of Mathematical Physics

Volumn 41, Issue 7, 2000, Pages 4478-4496

  Jung, Klaus ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034371070     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533355     Document Type: Article

References (15)

1. A. Martinez, "Precise exponential estimates in adiabatic theory," J. Math. Phys. 35, 3889-3915 (1994).
2. K. Jung, "Adiabatik und Serniklassik bei Regularität vom Gevrey-Typ," Ph.D. thesis, Technical University Berlin, D 83, 1997.
3. A. Martinez, "Estimates on complex interactions in phase space," Math. Nachr. 167, 203-254 (1994).
4. S. Nakamura, "On Martinez' method of phase space tunneling," Rev. Math. Phys. 7, 431-441 (1995).
5. G. B. Folland, Harmonic Analysis in Phase Space (Princeton University Press, Princeton, 1989).
6. A. Melin and J. Sjöstrand, "Fourier integral operators with complex-valued phase functions," Lect. Notes Math. 459, 120-223 (1975).
7. L. Rodino, Linear Partial Differential Operators in Gevrey Spaces (World Scientific, Singapore, London, Hong Kong, 1993).
8. M. Gevrey, "Sur la Nature Analytique des Solutions des Équations aux Dérivées Partielles," Annal. École Norm. Sup. 35, 129-189 (1918).
9. L. Hörmander, The Analysis of Linear Partial Differential Operators II (Springer, Berlin, Heidelberg, 1983).
10. Encyclopedic Dictionary of Mathematics, 2nd ed., Mathematical Society of Japan, edited by K. Itô (MIT Press, Cambridge, London, 1993).
11. J. Leray and Y. Ohya, "Systèmes linéaires, hperboliques non-stricts," Colloque C.B.M., Louvain, 1964, reprint in Battelle Rencontres on hyperbolic equations and waves, Seattle, Wisconsin, 283-322, 1968.
12. G. Nenciu, "Linear adiabatic theory: exponential estimates," Commun. Math. Phys. 152, 479-496 (1993).
13. M. V. Berry, "Semiclassical weak reflection above analytic and nonanalytic potential barriers," J. Phys. A 15, 3693-3704 (1982).
14. S. Nakamura, "Tunneling effects in momentum space and scattering," Lect. Notes Pure Appl. Math. 161, 131-151 (1994).
15. K. Jung, "Adiabatic invariance and the regularity of perturbations," Nonlinearity 8, 891-900 (1995).