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Języki publikacji
Abstrakty
In this paper, we study non-Archimedean Banach *-algebras Mp over the p-adic number fields Qp, and MQ over the adele ring AQ. We call elements of Mp, p-adic operators, for all primes p, respectively, call those of MQ, adelic operators. We characterize MQ in terms of Mp’s. Based on such a structure theorem of MQ, we introduce some interesting p-adic operators and adelic operators
Czasopismo
Rocznik
Tom
Strony
29--65
Opis fizyczny
Bibliogr. 20 poz.
Twórcy
autor
- St. Ambrose University Department of Mathematics 421 Ambrose Hall, 518 W. Locust St. Davenport, IA 52803, USA
Bibliografia
- [1] I. Cho, Operators induced by prime numbers, Methods Appl. Anal. 19 (2013) 4, 313–340.
- [2] I. Cho, Von Neumann algebras generated by the adele ring, (2012) (submitted).
- [3] I. Cho, Non-Archimedean matricial algebras induced by adelic structures, (2012) (submitted).
- [4] I. Cho, Free probability on arithmetic functions determined by primes, (2013) (submitted).
- [5] I. Cho, Classification on arithmetic functions and corresponding free-moment L-functions, Bulletin Korean Math. Soc. (2013) (to appear).
- [6] I. Cho, T. Gillespie, On the von Neumann algebra generated by the adele ring, (2013) (submitted).
- [7] I. Cho, P.E.T. Jorgensen, Krein-space operators induced by Dirichlet characters, Special Issues, Contemp. Math. American Math. Soc., (2013) (to appear).
- [8] I. Cho, P.E.T. Jorgensen, Krein-space representations of arithmetic functions determined by primes, (2013) (submitted).
- [9] T. Gillespie, Superposition of zeroes of automorphic L-functions and functoriality, PhD Thesis, Univ. of Iowa, (2010).
- [10] T. Gillespie, Prime number theorems for Rankin-Selberg L-functions over number fields, Sci. China Math. 54 (2011) 1, 35–46.
- [11] F. Radulescu, Random matrices, amalgamated free products and subfactors of the C_-algebra of a free group of nonsingular index, Invent. Math. 115 (1994), 347–389.
- [12] R. Speicher, Combinatorial theory of the free product with amalgamation and operator-valued free probability theory, Amer. Math. Soc. Mem. 132 (1998) 627.
- [13] D. Voiculescu, K. Dykemma, A. Nica, Free Random Variables, CRM Monograph Series, 1 (1992).
- [14] V.S. Vladimirov, I.V. Volovich, E.I. Zelenov, p-adic Analysis and Mathematical Physics, Ser. Soviet & East European Math. 1, World Scientific, 1994.
- [15] D. Bump, Automorphic Forms and Representations, Cambridge Studies in Adv. Math. 55, Cambridge Univ. Press, 1996.
- [16] P.R. Halmos, A Hilbert Space Problem Book (2nd ed.), Grad. Text in Math. 19, Springer-Verlag, 1982.
- [17] A. Kochubei, Non-Archimedean normal operators, J. Math. Phys. 51 (2010).
- [18] A. Kochubei, Non-Archimedean shift operators, ArXiv 1006.0077, (2010) (preprint).
- [19] A. Kochubei, Non-Archimedean unitary operators, ArXiv 1102.4302, (2011) (preprint).
- [20] A. Kochubei, On some classes of Non-Archimedean algebras, ArXiv 1206.2751, (2012) (preprint).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-34acdfa1-e2b5-45f1-ad66-0b4c8458fc27