Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Semi-classical behavior of the spectral function


Author: Ivana Alexandrova
Journal: Proc. Amer. Math. Soc. 134 (2006), 2295-2302
MSC (2000): Primary 35P05, 35S99
Published electronically: March 20, 2006
MathSciNet review: 2213702
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study the semi-classical behavior of the spectral function of the Schrödinger operator with short range potential. We prove that the spectral function is a semi-classical Fourier integral operator quantizing the forward and backward Hamiltonian flow relations of the system. Under a certain geometric condition we explicitly compute the phase in an oscillatory integral representation of the spectral function.


References [Enhancements On Off] (What's this?)

  • 1. Alexandrova, Ivana. Semi-Classical Wavefront Set and Fourier Integral Operators. To appear in Canadian Journal of Mathematics.
  • 2. Ivana Alexandrova, Structure of the semi-classical amplitude for general scattering relations, Comm. Partial Differential Equations 30 (2005), no. 10-12, 1505–1535. MR 2182302, 10.1080/03605300500299588
  • 3. Alexandrova, Ivana. Structure of the Short Range Amplitude for General Scattering Relations. Preprint mathAP/0411599 on arxiv.org.
  • 4. V. I. Arnold, Mathematical methods of classical mechanics, Springer-Verlag, New York-Heidelberg, 1978. Translated from the Russian by K. Vogtmann and A. Weinstein; Graduate Texts in Mathematics, 60. MR 0690288
  • 5. Laurent Michel, Semi-classical behavior of the scattering amplitude for trapping perturbations at fixed energy, Canad. J. Math. 56 (2004), no. 4, 794–824. MR 2074047, 10.4153/CJM-2004-036-2
  • 6. D. Robert and H. Tamura, Asymptotic behavior of scattering amplitudes in semi-classical and low energy limits, Ann. Inst. Fourier (Grenoble) 39 (1989), no. 1, 155–192 (English, with French summary). MR 1011982
  • 7. B. R. Vaĭnberg, Asymptotic methods in equations of mathematical physics, Gordon & Breach Science Publishers, New York, 1989. Translated from the Russian by E. Primrose. MR 1054376

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35P05, 35S99

Retrieve articles in all journals with MSC (2000): 35P05, 35S99


Additional Information

Ivana Alexandrova
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
Email: alexandr@math.toronto.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08463-2
Keywords: Semi-classical Schr\"{o}dinger operators, spectral function, Fourier integral operators.
Received by editor(s): March 1, 2005
Published electronically: March 20, 2006
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2006 American Mathematical Society