Noncommutative Mathematics for Quantum Systems

(Dana P.) #1

108 References


[Ban96] T. Banica. Theorie des repr ́ esentations du groupe quantique compact ́
libreO(n).C. R. Acad. Sci. Paris S ́er. I Math., 322: 241–244,
1996.


[Bel98] V.P. Belavkin. On quantum Ito algebras.ˆ Math. Phys. Lett., 7: 1–16,
1998.


[Bel08] S.T. Belinschi. The Lebesgue decomposition of the free additive
convolution of two probability distributions. Probab. Theory
Related Fields142(1-2): 125–150, 2008.


[BB04] S.T. Belinschi and H. Bercovici. Atoms and regularity for measures
in a partially defined free convolution semigroup.Math. Z.248(4):
665–674, 2004.


[BB05] S.T. Belinschi and H. Bercovici. Partially defined semigroups relative
to multiplicative free convolution.Int. Math. Res. Not., 2005(2):
65–101, 2005.


[Ber65] I. Berstein. On co-groups in the category of graded algebras.Trans.
Amer. Math. Soc.115 (1965), 257–269.


[Ber05a] H. Bercovici. Multiplicative monotonic convolution. Illinois J.
Math., 49(3): 929–951 (electronic), 2005.


[Ber05b] H. Bercovici. A remark on monotonic convolution.Infin. Dimens.
Anal. Quantum Probab. Relat. Top., 8(1): 117–120, 2005.


[Ber06] H. Bercovici. On Boolean convolutions. InOperator theory 20,
volume 6 ofTheta Ser. Adv. Math., pages 7–13. Theta, Bucharest,
2006.


[Ber98] J. Bertoin.L ́evy Processes. Cambridge University Press, 1998.


[BG01] A. Ben Ghorbal. Fondements alg ́ebrique des probabilit ́es
quantiques et calcul stochastique sur l’espace de Fock bool ́een.
PhD thesis, Universit ́e Henri Poincar ́e-Nancy 1, 2001.


[BGDS01] A. Ben Ghorbal and M. Schurmann. Quantum stochastic calculus ̈
on Boolean Fock space.Infin. Dimens. Anal. Quantum Probab.
Relat. Top., Vol. 7, No. 4, pp. 631–650, 2004.


[BGS99] A. Ben Ghorbal and M. Schurmann. On the algebraic foundations of ̈
a noncommutative probability theory. Prepublication 99/17, Institut ́
E. Cartan, Nancy, 1999.


[BGS02] A. Ben Ghorbal and M. Schurmann. Noncommutative notions of ̈
stochastic independence. Math. Proc. Cambridge Philos. Soc.,
133(3): 531–561, 2002.

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