Fourier expansion along geodesics on Riemann surfaces

Anton Deitmar

Open Mathematics (2014)

  • Volume: 12, Issue: 4, page 559-573
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Anton Deitmar. "Fourier expansion along geodesics on Riemann surfaces." Open Mathematics 12.4 (2014): 559-573. <http://eudml.org/doc/269044>.

@article{AntonDeitmar2014,
abstract = {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.},
author = {Anton Deitmar},
journal = {Open Mathematics},
keywords = {Closed geodesics; Fourier expansion; Trilinear products; Intertwining functionals; closed geodesics; trilinear products; intertwining functionals},
language = {eng},
number = {4},
pages = {559-573},
title = {Fourier expansion along geodesics on Riemann surfaces},
url = {http://eudml.org/doc/269044},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Anton Deitmar
TI - Fourier expansion along geodesics on Riemann surfaces
JO - Open Mathematics
PY - 2014
VL - 12
IS - 4
SP - 559
EP - 573
AB - 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.
LA - eng
KW - Closed geodesics; Fourier expansion; Trilinear products; Intertwining functionals; closed geodesics; trilinear products; intertwining functionals
UR - http://eudml.org/doc/269044
ER -

References

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  7. [7] Iwaniec H., Spectral Methods of Automorphic Forms, 2nd ed., Grad. Stud. Math., 53, American Mathematical Society, Providence, 2002 Zbl1006.11024
  8. [8] Knapp A.W., Representation Theory of Semisimple Groups, Princeton Landmarks Math., Princeton University Press, Princeton, 2001 Zbl0993.22001
  9. [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. [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 Zbl0703.35133

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