The non-Archimedean Laplace transform. (English) Zbl 0845.46047

De Grande-De Kimpe, N.; Khrennikov, A. Yu.

Bull. Belg. Math. Soc. - Simon Stevin 3, No. 2, 225-237 (1996).

Summary: Topological properties of the spaces of analytic test functions and distributions are investigated in the framework of the general theory of non-archimedean locally convex spaces. The Laplace transform, topological isomorphism, is introduced and applied to the differential equations of non-archimedean mathematical physics (Klein-Gordon and Dirac propagators).

MSC:

46S10	Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
46F12	Integral transforms in distribution spaces
44A10	Laplace transform
46F05	Topological linear spaces of test functions, distributions and ultradistributions

Keywords:

Klein-Gordon propagators; spaces of analytic test functions; distributions; non-archimedean locally convex spaces; Laplace transform; topological isomorphism; differential equations of non-archimedean mathematical physics; Dirac propagators