TY - JOUR UR - http://lib.ugent.be/catalog/pug01:525086 ID - pug01:525086 LA - eng TI - On rotationally symmetric Dirac equations and hypergeometric functions I PY - 2008 JO - (2008) ARCHIV DER MATHEMATIK SN - 0003-889X PB - IADUKSTRASSE 40-44 AU - Cação, Isabel AU - Constales, Denis TW16 801000631668 0000-0002-6826-6185 AU - Krausshar, Rolf AB - In this paper we establish an interesting relationship between the classical hypergeometric functions and solutions to a special class of radial symmetric higher dimensional Dirac type equations and describe how these equations can be solved fully analytically with methods from hypercomplex analysis. Concretely, let D := Sigma(n)(i=1) partial derivative/partial derivative x(i)e(i) be the Euclidean Dirac operator in the n-dimensional flat space R-n, E : = Sigma(n)(i=1) partial derivative/partial derivative x(i) the radial symmetric Euler operator and alpha and lambda be arbitrary non-zero complex parameters. We set up an explicit description of the Clifford algebra valued solutions to the PDE system [D -lambda - alpha xE] f(x) = 0 (x is an element of Omega subset of R-n) in terms of hypergeometric functions 2F(1) (a, b; c; z) of arbitrary complex parameters a, b and half-integer parameter c and special homogeneous polynomials. The regular solutions to the Dirac equation on the real projective space R-1,R-n which recently attracted much interest are recovered in the limit case lambda --> 0. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 525086 | ||
005 | 20180813143419.0 | ||
008 | 090319s2008------------------------eng-- | ||
022 | a 0003-889X | ||
024 | a 000256099000007 2 wos | ||
024 | a 1854/LU-525086 2 handle | ||
024 | a 10.1007/s00013-007-2475-x 2 doi | ||
040 | a UGent | ||
245 | a On rotationally symmetric Dirac equations and hypergeometric functions I | ||
260 | a IADUKSTRASSE 40-44, PO BOX 133, CH-4010 BASEL, SWITZERLAND b BIRKHAUSER VERLAG AG c 2008 | ||
520 | a In this paper we establish an interesting relationship between the classical hypergeometric functions and solutions to a special class of radial symmetric higher dimensional Dirac type equations and describe how these equations can be solved fully analytically with methods from hypercomplex analysis. Concretely, let D := Sigma(n)(i=1) partial derivative/partial derivative x(i)e(i) be the Euclidean Dirac operator in the n-dimensional flat space R-n, E : = Sigma(n)(i=1) partial derivative/partial derivative x(i) the radial symmetric Euler operator and alpha and lambda be arbitrary non-zero complex parameters. We set up an explicit description of the Clifford algebra valued solutions to the PDE system [D -lambda - alpha xE] f(x) = 0 (x is an element of Omega subset of R-n) in terms of hypergeometric functions 2F(1) (a, b; c; z) of arbitrary complex parameters a, b and half-integer parameter c and special homogeneous polynomials. The regular solutions to the Dirac equation on the real projective space R-1,R-n which recently attracted much interest are recovered in the limit case lambda --> 0. | ||
598 | a A1 | ||
700 | a Cação, Isabel | ||
700 | a Constales, Denis u TW16 0 801000631668 0 0000-0002-6826-6185 9 F43DD0B8-F0ED-11E1-A9DE-61C894A0A6B4 | ||
700 | a Krausshar, Rolf | ||
650 | a Mathematics and Statistics | ||
653 | a CLIFFORD ANALYSIS | ||
773 | t ARCHIV DER MATHEMATIK g Arch. Math. 2008. BIRKHAUSER VERLAG AG. 90 (5) p.440-449 q 90:5<440 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/525086/file/537543 z [ugent] y Cacao_2008_AM_90_5_440.pdf | ||
920 | a article | ||
Z30 | x EA 1 TW16 | ||
922 | a UGENT-EA |
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