Free Access
Issue
Math. Model. Nat. Phenom.
Volume 9, Number 5, 2014
Spectral problems
Page(s) 170 - 176
DOI https://doi.org/10.1051/mmnp/20149511
Published online 17 July 2014
  1. M. Abramowitz, I. Stegun. Handbook of mathematical functions. National Bureau of Standards, 1964. [Google Scholar]
  2. N. Burq, F. Planchon, J. Stalker, S. Tahvildar-Zadeh. Strichartz estimates for the wave and Schrödinger equations with the inverse-square potential. J. Funct. Anal., 203 (2003), 519–549. [CrossRef] [MathSciNet] [Google Scholar]
  3. N. Burq, F. Planchon, J. Stalker, S. Tahvildar-Zadeh. Strichartz estimates for the wave and Schrödinger equations with potentials of critical decay. Indiana Univ. Math. J., 53 (2004), 1665–1680. [CrossRef] [MathSciNet] [Google Scholar]
  4. N. Dunford, J.T. Schwartz. Linear Operators, Part II. New York, 1988. [Google Scholar]
  5. A. Erdelyi: Tables of integral transforms, Vol. 2. McGraw-Hill New York, 1954. [Google Scholar]
  6. M. B. Erdogan, W. R. Green. A weighted dispersive estimate for Schrödinger operators in dimension two. Comm. Math. Phys., 319 (2013), 791–811. [CrossRef] [MathSciNet] [Google Scholar]
  7. L. Fanelli, V. Felli, M. A. Fontelos, A. Primo. Time decay of scaling critical electromagnetic Schrödinger flows. Comm. Math. Phys., 324 (2013), 1033–1067. [CrossRef] [MathSciNet] [Google Scholar]
  8. M. Goldberg. Transport in the one-dimensional Schrödinger equation. Proc. Amer. Math. Soc., 135 (2007), 3171–3179. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Goldberg, W. Schlag. Dispersive estimates for Schrödinger operators in dimensions one and three. Comm. Math. Phys., 251 (2004), 157–178. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Goldberg, L. Vega, N Visciglia. Counterexamples of Strichartz inequalities for Schrödinger equations with repulsive potentials. Int. Math Res. Not, (2006), article ID 13927. [Google Scholar]
  11. G. Grillo, H. Kovařík. Weighted dispersive estimates for two-dimensional Schrödinger operators with Aharonov-Bohm magnetic field. J. Differential Equations, 256 (2014), 3889–3911. [Google Scholar]
  12. A. Jensen, T. Kato. Spectral properties of Schrödinger operators and time-decay of the wave functions. Duke Math. J., 46 (1979), 583–611. [CrossRef] [MathSciNet] [Google Scholar]
  13. A. Jensen, G. Nenciu. Schrödinger operators on the half line: Resolvent expansions and the Fermi golden rule at thresholds. Proc. Indian Acad. Sci. Math. Sci., 116 (2006), 375–392. [CrossRef] [MathSciNet] [Google Scholar]
  14. H. Kovařík. Heat kernels of two-dimensional magnetic Schrödinger and Pauli operators. Calc. Var. Partial Differential Equations, 44 (2012), 351–374. [CrossRef] [MathSciNet] [Google Scholar]
  15. P.D. Milman, Yu. A. Semenov. Heat kernel bounds and desingularizing weights. J. Funct. Anal., 202 (2003), 1–24. [CrossRef] [MathSciNet] [Google Scholar]
  16. P.D. Milman, Yu. A. Semenov. Global heat kernel bounds via desingularizing weights. J. Funct. Anal., 212 (2004), 373–398. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Murata. Asymptotic expansions in time for solutions of Schrödinger-type equations. J. Funct. Anal., 49 (1982), 10–56. [CrossRef] [MathSciNet] [Google Scholar]
  18. W. Schlag. Dispersive estimates for Schrödinger operators in dimension two. Comm. Math. Phys., 257 (2005), 87–117. [CrossRef] [MathSciNet] [Google Scholar]
  19. W. Schlag. Dispersive estimates for Schrödinger operators: a survey. Mathematical aspects of nonlinear dispersive equations. 255-285, Ann. of Math. Stud., 163, Princeton Univ. Press, Princeton, NJ, 2007. [Google Scholar]
  20. G. Teschl. Mathematical Methods in Quantum Mechanics With Applications to Schrödinger Operators. American Mathematical Society Providence, Rhode Island, 2009. [Google Scholar]
  21. X.P. Wang. Asymptotic expansion in time of the Schrödingier group on conical manifolds. Ann. Inst. Fourier, 56 (2006), 1903–1945. [CrossRef] [MathSciNet] [Google Scholar]
  22. R. Weder. Lp-Lp’ Estimates for the Schrödinger Equation on the Line and Inverse Scattering for the Nonlinear Schrödinger Equation with a Potential. J. Funct. Anal., 170 (2000), 37–68. [CrossRef] [MathSciNet] [Google Scholar]
  23. R. Weder. The Lp-Lp estimate for the Schrödinger equation on the half-line. J. Math. Anal. Appl., 281 (2003), 233–243. [CrossRef] [Google Scholar]

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