Mathematisches Institut

  Books and Monographs
  • Unbounded Operator Algebras and Representation Theory. Akademie-Verlag Berlin and Birkhäuser-Verlag Basel, 1990. 380pp
  • (with A.U. Klimyk) Quantum Groups and Their Representations. Texts and Monographs in Physics, Springer-Verlag Heidelberg, 1997. 552 pp. Errata
  • Unbounded self-adjoint operators on Hilbert space. Graduate Texts in Mathematics, 265. Springer, Dordrecht, 2012. xx+432 pp.

    Noncommutative real algebraic geometry
  • A strict Positivstellensatz for the Weyl algebra. Math. Ann. 331, 779-794; arxiv
  • A strict Positivstellensatz for Enveloping algebras. Math. Z. 254 (2006) 641-653; Erratum: Math. Z. 259(2008) 231; arxiv
  • Noncommutative real algebraic geometry—some basic concepts and first ideas. Emerging applications of algebraic geometry, 325–350, IMA Vol. Math. Appl., 149, Springer, New York, 2009; arxiv
  • Algebras of fractions and strict Positivstellensätze for -algebras. J. Reine Angew. Math. 647 (2010), 57–86.; arxiv
  • (with Yu. Savchuk) A noncommutative version of the Fejér-Riesz theorem.  Proc. Amer. Math. Soc. 138 (2010), 1243–1248; arxiv
  • (with Yu. Savchuk) Positivstellensätze for algebras of matrices. Linear Algebra Appl. 436 (2012), 758–788.
  • Around Hilbert's 17th problem. In Optimization stories, Editor M. Grötschel, Documenta Mathematica, Extra Volume ISMP (2012) 433–438.
  • (with J. Cimpric and Yu. Savchuk), On q-normal operators and quantum complex plane. To appear in Trans. Amer. Math. Soc. [arXiv]
    Quantum groups and noncommutative geometry
  • (with A. Schüler) Classification of bicovariant differential calculi on quantum groups of type A,B,C and D. Commun. Math. Phys. 167, 635-670 (1995).
  • (with A.Schüler) Classification of bicovariant differential calculi on quantum linear groups. Commun. Math. Phys. 170, 315-335 (1995).
  • (with A. Schüler) Left-covariant differential calculi on SLq(2) and SLq(3). J. Geom. Phys. 20, 87-115 (1996)
  • (with I. Heckenberger) Levi-Civita connections on the quantum groups SLq(N), Oq(N) and Spq(N). Commun. Math. Phys. 185, 177-196 (1997)
  • (with I. Heckenberger) Classification of bicovariant differential calculi on the quantum groups SLq(n+1) and Spq(2n). J. Reine Angew. Math. 502, 141-162 (1998)
  • Commutator representations of differential calculi on the quantum group SUq(2). J. Geom. Phys. 31, 241-264 (1999)
  • A polar decomposition for holomorphic functions on a strip. Bull. London Math. Soc.  33, 309-319 (2001)
  • Commutator representations of covariant differential calculi on quantum groups. Lett. Math. Phys. 59, 95-106 (2002)
  • The quantum quarter plane and the real quantum plane. Internat. J. Math. 13, 279-321 (2002)
  • (with E. Wagner) Examples of twisted cyclic cocycles from covariant differetial calculi. Lett. Math. Phys. 64, 245-254 (2003)
  • (with E. Wagner) Dirac operator and a twisted cyclic cocycle on the standard Podles quantum sphere. J. Reine Angew. Math. 574, 219-235 (2004)
  • (with V. L. Ostrovskyi) A resolvent approach to the real quantum plane. Preprint, 2013.
    Unbounded operators and unbounded representations
  • Integrable operator representations of R_q2, Xq, and SLq(2,R). Commun. Math. Phys. 159, 217-237 (1994)
  • Operator representations of Uq(sl_(R)). Lett. Math. Phys. 37, 211-222 (1996)
  • Operator representations of a q-deformed Heisenberg algebra. J. Math. Phys. 40, 4596-4604 (1999)
  • On well-behaved representations of *-algebras. J. Operator Theory 48, 287-502 (2002)
  • (with S. Ota) Some self-adjoint 2x2 operator matrices associated with closed operators. Integral Equations Operator Theory 45, 475-484 (2003)
  • (with E. Wagner) Hilbert space representations of cross product algebras. J. Funct. Anal.  200, 451-493 (2003)
  • (with E. Wagner) Hilbert space representations of cross product algebras II. Algebr. Repres. Theory 9(2006) 431-464; arXiv math.GA/0308229
  • (with E. Wagner) Representations of cross product algebras with Podles spheres, J. Lie Theory 17(2007)751-790; arXiv math.QA/0305309
  • (with Yu. Savchuk) Unbounded Induced Representations of *-Algebras. To appear in Algebras and Representation Theory; arxiv 
  • (with M. M. Malamud) Spectral theory of Schrödinger operators with infinitely many point interactions and radial positive definite functions. J. Funct. Anal. 263 (2012), 3144–3194. arxiv
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    Multidimensional moment problems
  • The K-moment problem for compact semi-algebraic sets. Math. Ann. 289, 203-206 (1991)
  • On determinacy notions for the two dimensional moment problem. Arkiv für Mat. 29, 277-284 (1991)
  • Non-commutative moment problems. Math. Z. 206, 623-650 (1991)
  • On the moment problem of closed semi-algebraic sets. J. Reine Angew. Math. 558, 225-234 (2003)
  • (with M. Putinar) Multivariate Determinateness. Indiana Univ. Math. J. 57, 2931-2986 (2008), arxiv