POISSON AND HEAT SEMIGROUPS FOR
THE BESSEL OPERATOR AND ON THE HYPERBOLIC SPACE
Adam Zakria1, Ibrahim-Elkhalil Ahmed2, Mohamed Vall Ould Moustapha3 1,2,3 Department of Mathematics
College of Arts and Sciences
Gurayat, Jouf University
Kingdom of SAUDI ARABIA 1 Department of Mathematics - Faculty of Sciences
University of Kordofan - El-Obeid, SUDAN 2 Shendi University, Faculty of Sciences and Technology
Department of Mathematics, Shendi, SUDAN 3 Faculté des Sciences et Techniques
Université de Nouakchott Al-Aasriya
Nouakchott - MAURITANIE
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References
[1] Y. Abdelhaye, M. Badahi , M.V. Ould Moustapha, Wave kernel for the
Schr¨odinger operator with the Morse potential and applications, F. J.
Math. Sci., 102 (2017), 1523-1532.
[2] J. Betancor, O. Ciaurri, T. Martnez, M. Perez, J.L. Torrea, J.L. Varona,
Heat and poisson semigroups for Fourier-Neumann expansions, J. Semi.
Forum., 73 (2006), 129142.
[3] U. Bunke, M. Olbrich, A. Juhl, The wave kernel for the Laplacian on
locally symmetric spaces of rank one, Theta functions, Trace formulas and
the Selberg zeta function, Ann. Global Anal. Geom., 12 (1994), 357-405.
[4] E.B. Davies, N. Mandouvalos, Heat kernel bounds on hyperbolic space and
Kleinian groups Proc. London Math. Soc., 3 (1988), 182-208.
[5] N. Ikeda, H. Matsumoto, Brownian motion one the hyperbolic plane and
Selberg trace formula, J. Funct. Anal., 163 (1999), 63-110.
[6] A. Intissar, M. V. Ould Moustapha, Solution explicite de l’´equation des
ondes dans un espace sym´etrique de type non compact de rang 1, C. R.
Acad. Sci. Paris., 321 (1995), 77-81.
[7] I. Cardoso, On the pointwise convergence to initial data of heat and Poisson
problems for the Bessel operator, J. Evol. Equ., 17 (2017), 953977.
[8] R.P. Lax, R.S. Phillips, The asymptotic distibution of lattice points in
Euclidean and non Euclidean spaces, J. Funct. Anal., 46 (1982), 280-350.
[9] N.N. Lebedev, Special Functions and Their Applications, Dover Publications
INC, New York (1972).
[10] N. Lohoue, Th. Rychener, Die Resolvente von auf symmetrischen R¨aumen
vom nichtkompakten, Typ. Comment. Math. Helv., 57 (1982), 445-468.
[11] W. Magnus, F. Oberhettinger, R.P. Soni, Formulas and Theorems for Special Functions of Mathematical Physics, Springer-Verlag Berlin Heidelberg,
New York (1966).
[12] P.M. Morse, Diatomic molecules according to the wave mechanics. II. Vibrational
levels, Phys. Rev., 34 (1929), 57-64.
[13] M.V. Ould Moustapha, Wave kernel with magnetic field on the hyperbolic
plane and with the Morse potential on the real line, Quantum Stud. Math.
Found., 7 (2020), 65-75.
[14] A.P. Prudnikov, Yu. A. Brychkov, O.I. Marichev, Special Functions, Integrals and Series, CRC Press, New York (1986).
[15] S. Keles, S. Bayrakci, Square-like functions generated by the Laplace-Bessel
differential operator, Adv. Diff. Equ., 281 (2014), 1687-1847.
[16] E.M. Stein, Singular Integrals and Differentiability Properties of Functions,
Princeton University Press, New Jersey (1970).
[17] R. Strichartz, A Guide to Distribution Theory and Fourier Transforms,
CRC Press, Boca Racon, Ann Arbor, London, Tokyo (1993).
[18] M. Taylor, Partial Differential Equations II, Springer, Applied Mathematics
in Sciences No.116, Second Edition (2011).