The theory of Mellin analytic functionals with unbounded carrier is developed. The generalized Mellin transform for such functionals is defined and applied to solve the Laplace-Beltrami type singular equations on a hyperbolic space. Then the asymptotic expansion of solutions is found.
@article{bwmeta1.element.bwnjournal-article-smv113i1p25bwm,
author = {Maria Pli\'s},
title = {Asymptotic expansion of solutions of Laplace-Beltrami type singular operators},
journal = {Studia Mathematica},
volume = {113},
year = {1995},
pages = {25-42},
zbl = {0827.46038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv113i1p25bwm}
}
Pliś, Maria. Asymptotic expansion of solutions of Laplace-Beltrami type singular operators. Studia Mathematica, Tome 113 (1995) pp. 25-42. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv113i1p25bwm/
[00000] [1] M. E. Pliś, The Mellin analytic functionals and the Laplace-Beltrami operator on the Minkowski half-plane, Studia Math. 99 (1991), 263-276. | Zbl 0743.46036
[00001] [2] M. E. Pliś and M. Sękowska, Mellin transform in Laplace-Beltrami equation, Opuscula Math. 5(1277) (1989), 109-116.
[00002] [3] Z. Szmydt and B. Ziemian, The Mellin Transformation and Fuchsian Type Partial Differential Equations, Kluwer Academic Publishers, 1992. | Zbl 0771.35002
[00003] [4] K. Yoshino, Some examples of analytic functionals and their transformations, Tokyo J. Math. 5 (1982), 479-490. | Zbl 0512.46043
[00004] [5] K. Yoshino, Lerch's theorem for analytic functionals with non-compact carrier and its applications to entire functions, Complex Variables Theory Appl. 2 (1984), 303-318. | Zbl 0512.30016