Papers

Unbounded operators

• On domains of powers of closed symmetric operators. J. Operator Theory 9(1983), 53–75. Correction: ibid 12(1984), 199.
• On restrictions of unbounded symmetric operators. J. Operator Theory 11(1984), 379–393.
• On commuting unbounded self–adjoint operators. Acata Math. Sci. (Szeged) 47(1984), 131–146.
• (with J. Friedrich) On commuting unbounded self-adjoint operators. II. J. Integral Equ. Operator Theory 7(1984), 815–867.
• On commuting unbounded self-adjoint operators. III. Manuscripta Math. 54(1985), 221–247.
• On commuting unbounded self-adjoint operators. IV. Math. Nachr. 125(1986), 83–102.
• A formally normal operator having no normal extension. Proc. Amer. Math. Soc. 95(1985), 503–504.
• Unbounded commutants and intertwining spaces of unbounded symmetric operators and *-repressentations. J. Funct. Analysis 71(1987), 47–68.
• (with Ota) On some classes of unbounded operators. Integral Equ. Operator Theory 12(1989), 211–226.
• (with Ota) Self–adjoint 2 x 2 operators matrices associated with closed operators. Integral Equ. Operator Theory 45(2003), 475–483.
• (with M. Malamud) Spectral theory of Schrödinger operators with infinitely many point interactions and radial positive definit functions. J. Funct. Analysis 263(2012), 3144–3194.
• (with R. Gebhardt) Unbounded operators on Hilbert C*-modules. Int. J. Math. 26(2015), 1550093, 48 pp.
• Unbounded operators on Hilbert C*-modules and C*-algebras. In: The diversity and beauty of applied operator theory. Oper. Theory Adv. Appl. 288(2018), 429–441.
• (with F. Gesztesy) On a theorem of Z. Sebestyen and Zs. Tarcsay. Acta Sci. Math. (Szeged) 85(2019), 291–293.
• Adjoint pairs and unbounded normal operators. Acta Sci. Math. (Szeged) 88(2022), 449–467.

Unbounded representations

• Integrable operator representations of R_q², X_qγ, and SL_q(2,R). Commun. Math. Phys. 159(1994), 217–237.
• Operator representations of U_q(sl_(R)). Lett. Math. Phys. 37(1996), 211–222.
• Operator representations of a q–deformed Heisenberg algebra. J. Math. Phys. 40(1999), 4596-4604.
• On well-behaved representations of *-algebras. J. Operator Theory 48(2002), 287–502.
• (with E. Wagner) Hilbert space representations of cross product algebras. J. Funct. Anal. 200(2003), 451-493.
• (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 Y. Savchuk) Unbounded induced representations of *-algebras. Algebras Repres. Theory 16(2013), 309-376.
• (with J. Cimpric and Y. Savchuk) On q-normal operators and the quantum complex plane. Trans. Amer. Math. Soc. 366(2014), 135–158.
• (with V. Ostrovskyi) A resolvent approach to the real quantum plane. Integral Equ. Operator Theory 79(2014), 451-476.
• Transition probabilities of positive functionals on *-algebras. J. Operator Theory 73(2015), 443-463.
• *-Bimodules. Proc. Amer. Math. Soc. 149(2021), 3923-3938.

Quantum groups and noncommutative differential calculi

• (with A. Schüler) Classification of bicovariant differential calculi on quantum groups of type A,B,C and D. Commun. Math. Phys. 167(1995), 635-670.
• (with A.Schüler) Classification of bicovariant differential calculi on quantum linear groups. Commun. Math. Phys. 170(1995), 315-335.
• (with A. Schüler) Left-covariant differential calculi on SL_q(2) and SL_q(3). J. Geom. Phys. 20(1996), 87–115.
• (with I. Heckenberger) Levi-Civita connections on the quantum groups SL_q(N), O_q(N) and Sp_q(N). Commun. Math. Phys. 185(1997), 177–196.
• (with I. Heckenberger) Classification of bicovariant differential calculi on the quantum groups SL_q(n+1) and Sp_q(2n). J. reine angew. Math. 502(1998), 141–162.
• Commutator representations of differential calculi on the quantum group SU_q(2). J. Geom. Phys. 31(1999), 241–264.
• On coquasitriangular bialgebras. Commun. Algebra 27 (1999), 4919-4928.
• A polar decomposition for holomorphic functions on a strip. Bull. London Math. Soc. 33(2001), 309-319.
• Commutator representations of covariant differential calculi on quantum groups. Lett. Math. Phys. 59(2002), 95–106.
• The quantum quarter plane and the real quantum plane. Internat. J. Math. 13(2002), 279-321.
• (with E. Wagner) Examples of twisted cyclic cocycles from covariant differetial calculi. Lett. Math. Phys. 64(2003), 245–254.
• (with E. Wagner) Dirac operator and a twisted cyclic cocycle on the standard Podles quantum sphere. J. reine angew. Math. 574(2004), 219–235.
• (with V. L. Ostrovskyi) A resolvent approach to the real quantum plane. Integral Equ. Operator Theory 79(2014), 451–476.

Real algebraic geometry

• The K-moment problem for compact semi-algebraic sets. Math. Ann. 289(1991), 203–206.
• Around Hilbert 17th problem. Doc. Math. 2012, Extra volume: Optimization stories, 433-438.
• (with M. Schötz) Positivstellensätze for semirings. Math. Ann. 2023.

Noncommutative real algebraic geometry

• A strict Positivstellensatz for the Weyl algebra. Math. Ann. 331(2005), 779-794.
• A strict Positivstellensatz for enveloping algebras. Math. Z. 254(2006), 641-653.
• Noncommutative real algebraic geometry- some basic concepts and first ideas. In: Emerging applications of algebraic geometry, 325-350. IMA volume 149, Springer, New York, 2009.
• Algebras of fractions and strict Positivstellensätze, J. reine angew. Math. 647(2010), 57-86.
• (with Y. Savchuk) A noncommutative version of the Fejer-Riesz theorem. Proc. Amer. Math. Soc. 138(2010), 1243–1248.
• (with Y. Savchuk) Positivstellensätze for algebras of matrices. Linear Algebra Appl. 436(2012), 758-788.
• (with J. Cimpric and Y. Savchuk) On q-normal operators and the complex quantum plane. Trans. Amer. Math. Soc. 366(2014), 135–158.

Multidimensional full moment problem

• The K-moment problem for comact semi-algebraic sets. Math. Ann. 289(1991), 203–206.
• On determinacy notions for the two-dimensional moment problem. Aktiv. Mat. 29(1991), 277–284.
• Non-commutative moment problems. Math. Z. 206(1991), 623-650.
• On the moment problem for closed semi-algebraic sets. J. reine angew. Math. 558(2003), 225–234.
• (with M. Putinar) Multivariate determinateness. Indiana Univ. Math. J. 57(2008), 2931–2986.
• A general fibre theorem for moment problems and some applications. Israel J. Math. 218(2017), 43-66.
• On the infinite-dimensional moment problem. Arkiv Mat. 56(2018), 441-459.
• Ten lectures on the moment problem. 81 pp. ArXiv 2008.12698
• The Stieltjes condition and multidimensional K-moment problem. Archiv Math. (Basel) 117(2021), 179–188.

Multidimensional truncated moment problem

• The multidimensional truncated moment problem: maximal masses. Methods Funct. Anal. Topology 21(2015), 266–281.
• (with B. Mourrain) Flat extesions on *-algebras. Proc. Amer. Math. Soc. 144(2016), 4873-4885.
• (with Ph. di Dio) The multidimensional truncated moment problem: Carathéodory numbers. J. Math. Anal. Appl. 461(2018), 1606–1638.
• (with Ph. di Dio) The multidimensional truncated moment problem: atoms, determinacy, core variety. J. Funct. Analysis 274(2018), 3124-3148.
• (with Ph. di Dio) The multidimensional truncated moment problem: the moment cone. J. Math. Anal. Appl. 511(2022), Nr. 1260066, 38 pp.