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Języki publikacji
Abstrakty
In this paper, we study semicircular-like elements, and semicircular elements induced by p-adic analysis, for each prime p. Starting from a p-adic number field Qp, we construct a Banach *-algebra [formula], for a fixed prime p, and show the generating elements Qpj of [formula] form weighted-semicircular elements, and the corresponding scalar-multiples Θpj of Qpj become semicircular elements, for all j ∈ Z. The main result of this paper is the very construction of suitable linear functionals [formula] on [formula], making Qpj be weighted-semicircular, for all j ∈ Z.
Czasopismo
Rocznik
Tom
Strony
665--703
Opis fizyczny
Bibliogr. 34 poz.
Twórcy
autor
- St. Ambrose University Department of Mathematics and Statistics 421 Ambrose Hall, 518 W. Locust St. Davenport, Iowa, 52803, USA
autor
- The University of Iowa Department of Mathematics 14 MacLean Hall Iowa City, IA 52242-1419, USA
Bibliografia
- [1] S. Albeverio, P.E.T. Jorgensen, A.M. Paolucci, Multiresolution wavelet analysis of integer-scale Bess el functions, J. Math. Phys. 48 (2007) 7, 073516, 24.
- [2] S. Albeverio, P.E.T. Jorgensen, A.M. Paolucci, On fractional Brownian motion and wavelets, Complex Anal. Oper. Theory 6 (2012) 1, 33-63.
- [3] D. Alpay, P.E.T. Jorgensen, Spectral theory for Gaussian processes: reproducing kernels, boundaries, and L,2-wavelet generators with fractional scales, Numer. Funct. Anal. Optim. 36 (2015) 10, 1239-1285.
- [4] D. Alpay, P.E.T. Jorgensen, D. Kimsey, Moment problems in an infinite number of variables, Infin. Dimens. Anal. Quantum Probab. Relat. Top. Prob. 18 (2015) 4, 1550024.
- [5] D. Alpay, P.E.T. Jorgensen, D. Levanony, On the equivalence of probability spaces, J. Theo. Prob. (2016), to appear.
- [6] D. Alpay, P.E.T. Jorgensen, G. Salomon, On free stochastic processes and their derivatives, Stochastic Process. Appl. 124 (2014) 10, 3392-3411.
- [7] I. Cho, Free distributional data of arithmetic functions and corresponding generating functions, Complex Anal. Oper. Theory 8 (2014) 2, 537-570.
- [8] I. Cho, Dynamical systems on arithmetic functions determined by prims, Banach J. Math. Anal. 9 (2015) 1, 173-215.
- [9] I. Cho, Free product C*-algebras induced by ^-algebras over p-adic number fields (2016), submitted.
- [10] I. Cho, T. Gillespie, Free probability on the Heche algebra, Complex Anal. Oper. Theory 9 (2015), 1491-1531.
- [11] I. Cho, P.E.T. Jorgensen, Krein-Space Operators Induced by Dirichlet Characters, Special Issues: Contemp. Math.: Commutative and Noncommutative Harmonic Analysis and Applications, Amer. Math. Soc. (2014), 3-33.
- [12] A. Connes, Noncommutative Geometry, Academic Press, San Diego, CA, 1994.
- [13] A. Connes, Hecke algebras, type Ill-factors, and phase transitions with spontaneous symmetry breaking in number theory, Selecta Math. (New Series) 1 (1995) 3, 411-457.
- [14] A. Connes, Trace formula in noncommutative geometry and the zeroes of the Riemann zeta functions, arXiv:math/9811068 [math.NT] (1998).
- [15] T. Gillespie, Superposition of zeroes of automorphic L-functions and functoriality, University of Iowa, PhD Thesis (2010).
- [16] T. Gillespie, Prime number theorems for Rankin-Selberg L-functions over number fields, Sci. China Math. 54 (2011) 1, 35-46.
- [17] P.E.T. Jorgensen, Operators and Representation Theory: Canonical Models for Algebras of Operators Arising in Quantum Mechanics, 2nd ed., Dover Publications, 2008.
- [18] P.E.T. Jorgensen, A.M. Paolucci, Wavelets in mathematical physics: q-oscillators, J. Phys. A. 36 (2003) 23, 6483-6494.
- [19] P.E.T. Jorgensen, A.M. Paolucci, States on the Cuntz algebras and p-adic random walks, J. Aust. Math. Soc. 90 (2011) 2, 197-211.
- [20] P.E.T. Jorgensen, A.M. Paolucci, q-frames and Bess el functions, Numer. Funct. Anal. Optim. 33 (2012) 7-9, 1063-1069.
- [21] P.E.T. Jorgensen, A.M. Paolucci, Markov measures and extended zeta functions, J. Appl. Math. Comput. 38 (2012) 1-2, 305-323.
- [22] 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.
- [23] F. Radulescu, Conditional expectations, traces, angles between spaces and representations of the Hecke algebras, Lib. Math. 33 (2013) 2, 65-95.
- [24] F. Radulescu, Free group factors and Hecke operators, notes taken by N. Ozawa, Proceedings of the 24th Conference in Operator Theory, Theta Advanced Series in Math., Theta Foundation, 2014.
- [25] R. Speicher, Multiplicative functions on the lattice of non-crossing partitions and free convolution, Math. Ann. 298 (1994), 611-628.
- [26] R. Speicher, Combinatorial theory of the free product with amalgamation and operator-valued free probability theory, Amer. Math. Soc. Mem. 132 (1998) 627.
- [27] R. Speicher, A conceptual proof of a basic result in the combinatorial approach to freeness, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 3 (2000), 213-222.
- [28] R. Speicher, P. Neu, Physical Applications of Freeness, Xll-th International Congress of Math. Phy. (ICMP '97), International Press, 1999, 261-266.
- [29] V.S. Vladimirov, p-adic quantum, mechanics, Comm. Math. Phys. 123 (1989) 4, 659-676. [30] V.S. Vladimirov, LV. Volovich, E.I. Zelenov, p-Adic Analysis and Mathematical Physics, Ser. Soviet & East European Math., vol. 1, World Scientific, 1994.
- [31] D. Voiculescu, Free probability and the von Neumann algebras of free groups, Rep. Math. Phys. 55 (2005) 1, 127-133.
- [32] D. Voiculescu, Symmetries arising from free probability theory, Frontiers in Number Theory, Physics and Geometry (2006), 231-243.
- [33] D. Voiculescu, Aspects of free analysis, Jpn. J. Math. 3 (2008) 2, 163-183.
- [34] D. Voiculescu, K. Dykemma, A. Nica, Free Random Variables, CRM Monograph Series, vol. 1, 1992.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-eb64f77b-2c75-449c-b0dc-9e9d55a03f0b