Back
 AM  Vol.5 No.16 , September 2014
Heat, Resolvent and Wave Kernels with Multiple Inverse Square Potential on the Euclidian Space Rn
Abstract: In this paper, the heat, resolvent and wave kernels associated to the Schr?dinger operator with multi-inverse square potential on the Euclidian space Rn are given in explicit forms.
Cite this paper: Ould Moustapha, M. (2014) Heat, Resolvent and Wave Kernels with Multiple Inverse Square Potential on the Euclidian Space Rn. Applied Mathematics, 5, 2612-2618. doi: 10.4236/am.2014.516249.
References

[1]   Boyer, C.P. (1976) Lie Theory and Separation of Variables for the Equation . SIAM Journal on Mathematical Analysis, 7, 230-263.
http;//dx.doi.org/10.1137/0507019

[2]   Ould Moustapha, M.V. (2014) The Heat, Resolvent and Wave Kernels with Bi-Inverse Square Potential on the Euclidean Plane. International Journal of Applied Mathematics, 27, 127-136.

[3]   Temme, N.M. (1996) Special Functions: An Introduction to the Classical Functions of Mathematical Physics. John Wiley and Sons, Inc., New-York.

[4]   Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F.G. (1954) Transcendental Functions, Tome II. New York.

[5]   Magnus, W., Oberhettinger, F. and Soni, R.P. (1966) Formulas and Theorems for the Special Functions of Mathematical Physics. Springer-Verlag, New York.
http;//dx.doi.org/10.1007/978-3-662-11761-3

[6]   Appell, P. and Kampe de Feriet, M.J. (1926) Fonctions Hypergeometriques et Hyperspheriques. Polyn?me d’Hermite. Gauthier-Villars, Paris.

[7]   Calin, O., Chang, D., Furutani, K. and Iwasaki, C. (2011) Heat Kernels for Elliptic and Sub-Elliptic Operators Methods and Techniques. Springer, New York.
http;//dx.doi.org/10.1007/978-0-8176-4995-1

[8]   Cheeger, J. and Taylor, M. (1982) On the Diffraction of Waves by Canonical Singularites I. Communications on Pure and Applied Mathematics, 35, 275-331.
http;//dx.doi.org/10.1002/cpa.3160350302

[9]   Strichartz, R. (2003) A Guide to Distribution Theory and Fourier Transform, Studies in Advanced Mathematics. CRC Press, Boca Racon.

[10]   Greiner, P.C., Holocman, D. and Kannai, Y. (2002) Wave Kernels Related to the Second Order Operator. Duke Mathematical Journal, 114, 329-387.
http;//dx.doi.org/10.1215/S0012-7094-02-11426-4

[11]   Burg, N., Planchon, F., Stalker, J. and Tahvildar-Zadeh, A.S. (2002) Strichartz Estimate for the Wave Equation with the Inverse Square Potential. arXiv:math.AP/0207152v3.

[12]   Planchon, F., Stalker, J. and Tahvildar-Zadeh, A.S. (2003) Dispersive Estimate for the Wave Equation with the Inverse Square Potential. Discrete and Continuous Dynamical Systems, 9, 1337-1400.

 
 
Top