Mehler's formula and functional calculus Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday
|
摘要
We show that Mehler's formula can be used to handle several formulas involving the quantization of singular Hamiltonians. In particular, we diagonalize in the Hermite basis the Weyl quantization of the characteristic function of several domains of the phase space.
We show that Mehler's formula can be used to handle several formulas involving the quantization of singular Hamiltonians. In particular, we diagonalize in the Hermite basis the Weyl quantization of the characteristic function of several domains of the phase space.
We show that Mehler's formula can be used to handle several formulas involving the quantization of singular Hamiltonians. In particular, we diagonalize in the Hermite basis the Weyl quantization of the characteristic function of several domains of the phase space.
引文
1 Amour L,Jager L,Nourrigat J.Lower bounds for pseudodifferential operators with a radial symbol.J Math Pures Appl(9),2015,103:1157-1162
2 Askey R,Gasper G.Positive Jacobi polynomial sums.II.Amer J Math,1976,98:709-737
3 Feldheim E.D′eveloppments en s′erie de polynomes d’Hermite et de Laguerre`a l’aide des transformations de Gauss et de Henkel.III.Proc Kon Ned Akad Wet,1940,43:379-386
4 Flandrin P.Maximum signal energy concentration in a time-frequency domain.In:Proceedings of IEEE International Conference on Acoustics,Speech,and Signal Processing.New York:IEEE,1988,2176-2179
5 Flandrin P.Time-Frequency/Time-Scale Analysis.Wavelet Analysis and Its Applications,vol.10.San Diego:Academic Press,1999
6 Hlawatsch F,Flandrin P.The interference structure of the Wigner distribution and related time-frequency signal representations.In:The Wigner Distribution.Amsterdam:Elsevier,1997,59-133
7 H¨ormander L.Symplectic classification of quadratic forms,and general Mehler formulas.Math Z,1995,219:413-449
8 H¨ormander L.The Analysis of Linear Partial Differential Operators.III.Classics in Mathematics.Berlin:Springer,2007
9 Lerner N.Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators.Pseudo-Differential Operators Theory and Applications,vol.3.Basel:Birkh¨auser Verlag,2010
10 Lieb E H,Ostrover Y.Localization of multidimensional Wigner distributions.J Math Phys,2010,51:102101
11 Unterberger A.Oscillateur harmonique et op′erateurs pseudo-diff′erentiels.Ann Inst Fourier(Grenoble),1979,29:201-221
2 Askey R,Gasper G.Positive Jacobi polynomial sums.II.Amer J Math,1976,98:709-737
3 Feldheim E.D′eveloppments en s′erie de polynomes d’Hermite et de Laguerre`a l’aide des transformations de Gauss et de Henkel.III.Proc Kon Ned Akad Wet,1940,43:379-386
4 Flandrin P.Maximum signal energy concentration in a time-frequency domain.In:Proceedings of IEEE International Conference on Acoustics,Speech,and Signal Processing.New York:IEEE,1988,2176-2179
5 Flandrin P.Time-Frequency/Time-Scale Analysis.Wavelet Analysis and Its Applications,vol.10.San Diego:Academic Press,1999
6 Hlawatsch F,Flandrin P.The interference structure of the Wigner distribution and related time-frequency signal representations.In:The Wigner Distribution.Amsterdam:Elsevier,1997,59-133
7 H¨ormander L.Symplectic classification of quadratic forms,and general Mehler formulas.Math Z,1995,219:413-449
8 H¨ormander L.The Analysis of Linear Partial Differential Operators.III.Classics in Mathematics.Berlin:Springer,2007
9 Lerner N.Metrics on the Phase Space and Non-Selfadjoint Pseudo-Differential Operators.Pseudo-Differential Operators Theory and Applications,vol.3.Basel:Birkh¨auser Verlag,2010
10 Lieb E H,Ostrover Y.Localization of multidimensional Wigner distributions.J Math Phys,2010,51:102101
11 Unterberger A.Oscillateur harmonique et op′erateurs pseudo-diff′erentiels.Ann Inst Fourier(Grenoble),1979,29:201-221