A p-adic theory of hyperfunctions. I. (English) Zbl 0457.12010

Morita, Yasuo

Publ. Res. Inst. Math. Sci. 17, 1-24 (1981).

MSC:

12J25	Non-Archimedean valued fields
46F15	Hyperfunctions, analytic functionals
11S80	Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
46S10	Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
11S40	Zeta functions and \(L\)-functions

Keywords:

p-adic hyperfunctions; non archimedean valuated field; integral representation of p-adic L-function

References:

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[26]	Volkenborn, A., On generalized p-adic integration, Bull. Soc. Math. France, Me”moire 39-40 (1974), 375-384. (2) After writing the present paper, the author” proved that the Krasner theory and the Tate theory give the same results if the field k is maximally complete and the domain D is a completely regular quasi-connected set. Furthermore, he proved that we can obtain the results of Section 1 without assuming that k is maximally complete if we use the Tate theory instead of the Krasner theory. Hence [17] will not appear. For the references and the details, see Morita,. Y., Analytic functions on an open subset of P*<*), /. reine u. angew. Math., 311/312 (1979), 361-383.