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Heat, Resolvent and Wave Kernels with Multiple Inverse Square Potential on the Euclidian Space R<sup>n</sup>
Unité de Recherche: Analyse, EDP et Modélisation (AEDPM), Département de Mathématiques et Informatique, Faculté des Sciences et Techniques, Universitè des Sciences, de Technologie et de la Médecine (USTM), Nouakchott, Mauritanie
- 1 Unité de Recherche: Analyse, EDP et Modélisation (AEDPM), Département de Mathématiques et Informatique, Faculté des Sciences et Techniques, Universitè des Sciences, de Technologie et de la Médecine (USTM), Nouakchott, Mauritanie
Applied Mathematics·Volume 05 (2014)·Pages 2612–2618·Published 29 August 2014·DOI10.4236/am.2014.516249
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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 R n are given in explicit forms.
KeywordsHeat KernelWave KernelResolvent KernelMultiple-Inverse Square PotentialBessel FunctionLauricella Hypergeometric Function
- 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
- 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.
- Temme, N.M. (1996) Special Functions: An Introduction to the Classical Functions of Mathematical Physics. John Wiley and Sons, Inc., New-York.
- Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F.G. (1954) Transcendental Functions, Tome II. New York.
- 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
- Appell, P. and Kampe de Feriet, M.J. (1926) Fonctions Hypergeometriques et Hyperspheriques. Polyn?me d’Hermite. Gauthier-Villars, Paris.
- 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
- 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
- Strichartz, R. (2003) A Guide to Distribution Theory and Fourier Transform, Studies in Advanced Mathematics. CRC Press, Boca Racon.
- 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
- 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.
- 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.