Dr. Rolf Gohm - Homepage

Research Interests

• Noncommutative Probability Theory
  
• Operator Algebras
  
• Operator Theory
  
• Quantum Control

Talks

• Noncommutative independence from the infinite Braid Group and Symmetric Group (Chennai, 10 August 2010)
  
  
• Transfer Functions associated to Markov Chains (Bangalore, 14 August 2010)

Publications and Preprints

• Verbandstheoretische Charakterisierungen von Hilberträumen (Characterizing Hilbert space by its lattice of subspaces), Diplomarbeit, Stuttgart (1987)
  
  
• Untersuchungen über polynomiale Beschränktheit und einige spektraltheoretische Anwendungen (Polynomial boundedness and applications to spectral theory), Dissertation (PhD), Tübingen (1992)
  
  
• A spectral classification of operators related to polynomial boundedness , Journal of Operator Theory 36 (1996), 249-281
  
  
• Adapted endomorphisms which generalize Bogoljubov transformations , Journal of Operator Theory 45 (2001), 19-37
  
  
• Prediction errors and completely positive maps , in: Quantum Probability and Inf.Dim.Analysis; Proceedings Burg 2001, QP-PQ vol. XV, World Scientific (2003), 107-119
  
  
• A duality between extension and dilation , in: Advances in quantum dynamics, ed. G. Price et al., Contemp. Math. 335, Amer. Math. Soc. (2003), 139--147
  
  
• Kümmerer-Maassen scattering theory and entanglement , Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol.7(2), World Scientific (2004), 271-280
  
  
• Elements of a spatial theory for non-commutative stationary processes with discrete time index, Habilitation Thesis (2002)
  A revised version appeared as Noncommutative Stationary Processes , Lecture Notes in Mathematics 1839 , Springer-Verlag (2004)
  
  
• with M.Skeide, Constructing extensions of CP-maps via tensor dilations with the help of von Neumann modules , Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol.8(2), World Scientific (2005), 291-305
  
  
• with U.Franz, Random walks on finite quantum groups , Quantum Independent Increment Processes: Quantum Levy Processes, Classical Probability and Applications, Eds. U. Franz and M. Schürmann, Lecture Notes in Mathematics 1866 , Springer-Verlag (2005), 1-32
  
  
• A probabilistic index for completely positive maps and an application , Journal of Operator Theory 54(2) (2005), 339-361
  
  
• Geometric properties of the set of extensions of a stochastic matrix , Infinite Dimensional Harmonic Analysis III, Eds. H. Heyer et al., World Scientific (2005), 59-70
  
  
• with B.Kümmerer, T.Lang, Noncommutative symbolic coding , Ergodic Theory and Dynamical Systems 26 (2006), 1521-1548
  
  
• Decompositions of Beurling type for E_0-semigroups , Banach Center Publications, Vol. 73, Institute of Mathematics, Polish Academy of Sciences, Warzawa (2006), 167-176
  
  
• with S.Dey, Characteristic functions for ergodic tuples , Integral Equations and Operator Theory 58 (2007), 43-63
  
  
• with J.Gough, M.Yanagisawa Linear quantum feedback networks , Phys. Rev. A 78, 062104 (2008)
  
  
• with C.Köstler, Noncommutative independence from the braid group , Comm. Math. Phys., vol.289(2) (2009), 435-482
  
  
• Non-commutative Markov chains and multi-analytic operators , J. Math. Anal. Appl., vol.364(1) (2009), 275-288
  
  
• with S.Dey, Characteristic functions of liftings , Journal of Operator Theory 65 (2011), 17-45
  
  
• with C.Köstler, Noncommutative independence from characters of the infinite symmetric group , preprint
  
  
• with C.Köstler, Noncommutative independence in the infinite braid and symmetric group , preprint
  
  
• Transfer Functions for Pairs of Wandering Subspaces , preprint