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Original Articles

A unitary joint eigenfunction transform for the AΔOs exp(ia±d/dz)+exp(2πz/a)

Pages 253-294 | Published online: 21 Jan 2013

References

  • Volkov A Yu Noncommutative hypergeometry, arXiv:math.QA/0312084
  • Barnes E W The theory of the double gamma function, Phil. Trans. Roy. Soc. A 196 (1901), 265–388
  • Ruijsenaars S N M Systems of Calogero-Moser type, in Proceedings of the 1994 Banff summer school Particles and fields, CRM Ser. in Math. Phys., Editors: Semenoff G and Vinet L, Springer, New York, 1999, 251–352
  • Ruijsenaars S N M First order analytic difference equations and integrable quantum systems, J. Math. Phys. 38 (1997), 1069–1146
  • Faddeev L D Discrete Heisenberg-Weyl group and modular group, Lett. Math. Phys. 34 (1995), 249–254
  • Woronowicz S L Quantum exponential function, Rev. Math. Phys. 12 (2000), 873–920
  • Faddeev L D Modular double of a quantum group, in Conférence Moshé Flato 1999 (Dijon), Vol I, Math. Phys. Stud. 21, Kluwer, Dordrecht, 2000, 149–156
  • Faddeev L D Kashaev R M Volkov A Yu Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality, Commun. Math. Phys. 219 (2001), 199–219
  • Ruijsenaars S N M Sine-Gordon solitons vs. relativistic Calogero-Moser particles, in Proceedings of the Kiev NATO Advanced Study Institute “Integrable structures of exactly solvable two-dimensional models of quantum field theory”, Editors: Pakuliak S and von Gehlen G, NATO Science Series 35, Kluwer, Dordrecht, 2001, 273–292
  • Kharchev S Lebedev D Semenov-Tian-Shansky M Unitary representations of U q (sl(2, ℝ), the modular double and the multiparticle q-deformed Toda chains, Commun. Math. Phys. 225 (2002), 573–609
  • Van de Bult F J Ruijsenaars’ hypergeometric function and the modular double of U q (sl 2(ℂ)), arXiv:math.QA/0501405
  • Reed M Simon B Methods of Modern Mathematical Physics. I. Functional analysis, Academic Press, New York, 1972
  • Reed M Simon B Methods of Modern Mathematical Physics. II. Fourier analysis, Selfadjointness, Academic Press, New York, 1975
  • Ruijsenaars S N M A generalized hypergeometric function III. Associated Hilbert space transform, Commun. Math. Phys. 243 (2003), 413–448
  • Ruijsenaars S N M A new class of reflectionless second-order AΔOs and its relation to nonlocal solitons, Regular and Chaotic Dynamics 7 (2002), 351–391
  • Ruijsenaars S N M Isometric reflectionless eigenfunction transforms for higher-order AΔOs, Calogero Festschrift issue, J. Nonlinear Math. Phys. 12 Suppl. 1 (2005), 565–598
  • Ruijsenaars SNM A generalized hypergeometric function satisfying four analytic difference equations of Askey-Wilson type, Commun. Math. Phys. 206 (1999), 639–690
  • Reed M Simon B Methods of Modern Mathematical Physics. III. Scattering theory, Academic Press, New York, 1979
  • Bytsko A G Teschner J R-operator, co-product and Haar-measure for the modular double of U q (sl(2, ℝ)), Commun. Math. Phys. 240 (2003), 171–196
  • Shintani T On a Kronecker limit formula for real quadratic fields, J. Fac. Sci. Univ. Tokyo 24 (1977), 167–199
  • Kurokawa N Multiple sine functions and Selberg zeta functions, Proc. Japan Acad. A67 (1991), 61–64
  • Jimbo M Miwa T Quantum K Z equation with |q|=1 and correlation functions of the XXZ model in the gapless regime, J. Phys. A 29 (1996), 2923–2958
  • Nishizawa M Ueno K Integral solutions of q-difference equations of the hypergeometric type with |q|=1, in Proceedings of the Workshop Infinite analysis (1996) IIAS, Japan, arXiv:q-alg/9612014
  • Hölder O Ueber eine transcendente Function, Göttingen Nachr. 16 (1886), 514–522
  • Ruijsenaars S N M Scattering theory for the Federbush, massless Thirring and continuum Ising models, J. Func. Anal. 48 (1982), 135–171

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