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Fourier expansion along geodesics on Riemann surfaces

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For an eigenfunction of the Laplacian on a hyperbolic Riemann surface, the coefficients of the Fourier expansion are described as intertwining functionals. All intertwiners are classified. A refined growth estimate for the coefficients is given and a summation formula is proved.
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Bibliografia
  • [1] Bernstein J., Reznikov A., Analytic continuation of representations and estimates of automorphic forms, Ann. of Math., 1999, 150(1), 329–352 http://dx.doi.org/10.2307/121105
  • [2] Bernstein J., Reznikov A., Estimates of automorphic functions, Mosc. Math. J., 2004, 4(1), 19–37
  • [3] Deitmar A., Invariant triple products, Int. J. Math. Math. Sci., 2006, #48274
  • [4] Gangolli R., Varadarajan V.S., Harmonic Analysis of Spherical Functions on Real Reductive Groups, Ergeb. Math. Grenzgeb., 101, Springer, Berlin, 1988 http://dx.doi.org/10.1007/978-3-642-72956-0
  • [5] Gradshteyn I.S., Ryzhik I.M., Table of Integrals, Series, and Products, 7th ed., Elsevier/Academic Press, Amsterdam, 2007
  • [6] Harish-Chandra, Harmonic analysis on real reductive groups. I. The theory of the constant term, J. Functional Analysis, 1975, 19, 104–204 http://dx.doi.org/10.1016/0022-1236(75)90034-8
  • [7] Iwaniec H., Spectral Methods of Automorphic Forms, 2nd ed., Grad. Stud. Math., 53, American Mathematical Society, Providence, 2002
  • [8] Knapp A.W., Representation Theory of Semisimple Groups, Princeton Landmarks Math., Princeton University Press, Princeton, 2001
  • [9] Molčanov V.F., Tensor products of unitary representations of the three-dimensional Lorentz group, Izv. Akad. Nauk SSSR Ser. Mat., 1979, 43(4), 860–891 (in Russian)
  • [10] Seeger A., Sogge C.D., Bounds for eigenfunctions of differential operators, Indiana Univ. Math. J., 1989, 38(3), 669–682 http://dx.doi.org/10.1512/iumj.1989.38.38031
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bwmeta1.element.doi-10_2478_s11533-013-0366-x
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