Mathematische Zeitschrift

, Volume 265, Issue 2, pp 437–449 | Cite as

L p Wiener–Tauberian theorems for M(2)

  • E. K. NarayananEmail author
  • Rama Rawat


We prove two sided and one sided analogues of the Wiener-Tauberian theorem for the Euclidean motion group, M(2).


Wiener–Tauberian theorem Fourier transform Maximal ideals 

Mathematics Subject Classification (2000)

Primary 43A20 Secondary 22D15 


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  1. 1.
    Agranovsky M.L., Narayanan E.K.: L p-integrability, supports of Fourier transforms and uniqueness for convolution equations. J. Fourier Anal. Appl. 10(3), 315–324 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Gangolli R.: On the symmetry of L 1 algebras of locally compact motion groups, and the Wiener Tauberian theorem. J. Funct. Anal. 25, 244–252 (1977)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Leptin H.: Ideal theory in group algebras of locally compact groups. Invent. Math. 31(3), 259–278 (1975/76)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Leptin H.: On one sided harmonic analysis in non commutative locally compact groups. J. Reine. Angew. Math. 306, 122–153 (1979)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Rawat R., Sitaram A.: The injectivity of the Pompeiu transform and L p-analogues of the Wiener–Tauberian theorem. Israel J. Math. 91, 307–316 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Stein E.M., Weiss G.: Introduction to Fourier analysis of Euclidean spaces. Princeton University Press, Princeton (1971)Google Scholar
  7. 7.
    Stein E.M.: Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals. Princeton University Press, Princeton (1993)zbMATHGoogle Scholar
  8. 8.
    Sugiura M.: Unitary Representations and Harmonic Analysis. Kodansha Scientific books, Tokyo (1975)zbMATHGoogle Scholar
  9. 9.
    Szego, G.: Orthogonal polynomials. In: Amer. Math. Soc. Colloq. Publ. vol. 23, Amer. Math. Soc., Providence, RIGoogle Scholar
  10. 10.
    Weit Y.: On the one-sided Wiener’s theorem for the motion group. Ann. Math. 111, 415–422 (1980)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  2. 2.Department of MathematicsIndian Institute of Technology, KanpurKanpurIndia

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