Adelic analysis and functional analysis on the finite Adele ring

• Autorzy: Cho I.

Identyfikatory

DOI

10.7494/OpMath.2018.38.2.139

• Języki publikacji: EN

Abstrakty

EN

In this paper, we study operator theory on the *-algebra Mp, consisting of all measurable functions on the finite Adele ring Aq, in extended free-probabilistic sense. Even though our *-algebra Mp is commutative, our Adelic-analytic data and properties on Mv are understood as certain free-probabilistic results under enlarged sense of (noncommutative) free probability theory (well-covering commutative cases). From our free-probabilistic model on Aq, we construct the suitable Hilbert-space representation, and study a C*-algebra M-p generated by M-p under representation. In particular, we focus on operator-theoretic properties of certain generating operators on Mp.

Słowa kluczowe

EN

representations; C*-algebras; p-adic number fields; adele ring; finite Adele ring

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2018
• Tom: Vol. 38, no. 2
• Strony: 139--185
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Cho I.

• Saint Ambrose University Department ol Mathematics and Statistics 421 Ambrose Hall, 518 W. Locust St. Davenport, Iowa, 52803, USA

Bibliografia

• [1] I. Cho, Free distributional data of arithmetic functions and corresponding generating functions, Compl. Anal. Oper. Theo. 8 (2014) 2, 537-570.
• [2] I. Cho, Dynamical systems on arithmetic functions determined by prims, Banach J. Math. Anal. 9 (2015) 1, 173-215.
• [3] I. Cho, On dynamical systems induced by p-adic number fields, Opuscula Math. 35 (2015) 4, 445-484.
• [4] I. Clio, Representations and corresponding operators induced by Hecke algebras, Complex Anal. Oper. Theory 10 (2016) 3, 437-477.
• [5] I. Cho, Free semicircular families in free product Banach *-algebras induced by p-adic number fields, Complex Anal. Oper. Theory 11 (2017) 3, 507-565.
• [6] I. Cho, p-adic number fields acting on W* -probability spaces, Turkish J. Anal. Numb. Theo. (2017), to appear.
• [7] I. Cho, T. Gillespie, Free probability on the Hecke algebra, Complex Anal. Oper. Theory 9 (2015) 7, 1491-1531.
• [8] I. Cho, P.E.T. Jorgensen, Semicircular elements induced by p-adic number fields, Opus-cula Math. 37 (2017) 5, 665-703.
• [9] T. Gillespie, Superposition of zeroes of automorphic L-functions and functoriality, PhD Thesis, Univ. ol Iowa, (2010).
• [10] T. Gillespie, Prime Number Theorems for Rank/in-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. 627 (1998).
• [13] V.S. Vladimirov, I.V. Volovich, E.I. Zelenov, p-Adic Analysis and Mathematical Physics, Ser. Soviet & East European Math., vol. 1, World Scientific, 1994.
• [14] D. Voiculescu, K. Dykemma, A. Nica, Free Random Variables, CRM Monograph Series, vol. 1, Amer. Math. Soc, Providence, 1992.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).