Manuscripta Mathematica

, Volume 140, Issue 1–2, pp 13–28 | Cite as

Spectral analysis on \({{\rm SL}(2, \mathbb{R})}\)

  • Sanjoy Pusti
  • Rudra P. SarkarEmail author


Let G be the group \({{\rm SL}(2, \mathbb{R})}\). For this group we prove a version of Schwartz’s theorem on spectral analysis for the group G. We find the sharp range of Lebesgue spaces L p (G) for which a smooth function is not mean periodic unless it is a cusp form. Failure of the Schwartz-like theorem is also proved when C (G) is replaced by L p (G) with suitable p. We show that the last result is linked with the failure of the Wiener-tauberian theorem for G.

Mathematics Subject Classification (2000)

Primary 43A85 Secondary 22E30 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  2. 2.Stat–Math UnitIndian Statistical InstituteKolkataIndia

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