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This article is cited in 6 scientific papers (total in 6 papers)
Generalized functions and Gaussian path integrals over non-archimedean function spaces
A. Yu. Khrennikov
Abstract:
A mathematical apparatus is developed for non-Archimedean physics: a theory of generalized functions, a theory of integration, and a harmonic analysis. Both finite-dimensional and infinite-dimensional non-Archimedean spaces are considered. Gaussian and Feynman path integrals on non-Archimedean function spaces are introduced. Quantization of a non-Archimedean scalar bosonic field is carried out in the formalism of path integrals. Linear differential equations in spaces of test functions and spaces of generalized functions on infinite-dimensional non-Archimedean spaces are studied (in particular, the heat equation and the Schrödinger equation with a potential).
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Mathematics of the USSR-Izvestiya, 1992, 39:1, 761–794
Bibliographic databases:
UDC:
517.948+530.1+517.2
MSC: Primary 58C50, 81S40, 46S10; Secondary 46F05, 46F12, 26E30, 81T30, 58F06, 35S05 Received: 12.10.1989
Citation:
A. Yu. Khrennikov, “Generalized functions and Gaussian path integrals over non-archimedean function spaces”, Izv. Akad. Nauk SSSR Ser. Mat., 55:4 (1991), 780–814; Math. USSR-Izv., 39:1 (1992), 761–794
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/izv988 http://mi.mathnet.ru/eng/izv/v55/i4/p780
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This publication is cited in the following articles:
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A. Yu. Khrennikov, M. Endo, “Unboundedness of a $p$-adic Gaussian distribution”, Russian Acad. Sci. Izv. Math., 41:2 (1993), 367–375
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S. S. Akbarov, “Smooth structure and differential operators on a locally compact group”, Izv. Math., 59:1 (1995), 1–44
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A. Kh. Bikulov, I. V. Volovich, “$p$-adic Brownian motion”, Izv. Math., 61:3 (1997), 537–552
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Youngho JANG, “Non-Archimedean quantum mechanics”, Tohoku Math Publ, 10:10 (1998), 1
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A. Yu. Khrennikov, “Laws of large numbers in non-Archimedean probability theory”, Izv. Math., 64:1 (2000), 207–219
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A. Yu. Khrennikov, H. Petersson, “A Paley–Wiener theorem for generalized entire functions on infinite-dimensional spaces”, Izv. Math., 65:2 (2001), 403–424
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