Noncommutative Mathematics for Quantum Systems

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118 References


[Sch00] M. Schurmann. ̈ Operator processes majorizing their quadratic
variation. Infin. Dimens. Anal. Quantum Probab. Relat. Top,
3(1): 99–120, 2000.


[Ske99] M. Skeide. Hunt’s Formula forSUq( 2 )– a Unified View. Open
Systems & Information Dynamics, 6(1): 1–28, 1999.


[Ske01] M. Skeide. Hilbert modules and applications in quantum probability.
Habilitation thesis, 2001.


[Sko91] A.V. Skorohod. Random Processes with Independent
Increments. Kluwer Academic Publishers, 1991. (Russian original
1986).


[Spe97] R. Speicher. Universal products. In D. Voiculescu, editor,Free
probability theory. Papers from a workshop on random matrices
and operator algebra free products, Toronto, Canada, March
1995 , volume 12 of Fields Inst. Commun., pages 257–266.
American Mathematical Society, Providence, RI, 1997.


[SS98] M. Schurmann and M. Skeide, Infinitesimal generators of the quantum ̈
group SUq( 2 ). Inf. Dim. Anal., Quantum Prob. and Rel.
Topics, 1(4): 573–598, 1998.


[SSV10] M. Sch ̈urmann, M. Skeide, and S. Volkwardt. Transformation of
quantum L ́evy processes on Hopf algebras.Commun. Stoch. Anal.,
4(4): 553–577, 2010.


[SV08] M. Schurmann and S. Voß. Positivity of free convolution semigroups. ̈
In:Quantum probability and related topics, volume 23 of QP–
PQ: Quantum Probab. White Noise Anal., pages 225–235. World Sci.
Publ., Hackensack, NJ, 2008.


[SV14] M. Schurmann and S. Voß. Schoenberg Correspondence on Dual ̈
Groups.Comm. Math. Phys.328 (2014), no. 2, 849–865.


[Str00] R.F. Streater. Classical and quantum probability. J. Math. Phys.,
41(6): 3556–3603, 2000.


[SW97] R. Speicher and R. Woroudi. Boolean convolution. In D. Voiculescu,
editor, Free probability theory. Papers from a workshop on
random matrices and operator algebra free products, Toronto,
Canada, March 1995, volume 12 ofFields Inst. Commun., pages
267–279. American Mathematical Society, Providence, RI, 1997.


[Swe69] M.E. Sweedler.Hopf Algebras. Benjamin, New York, 1969.


[Tim08] T. Timmermann.An invitation to quantum groups and duality.
From Hopf algebras to multiplicative unitaries and beyond.

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