Skip to main content
SpringerLink
Log in

On regularity of twisted spherical means and special Hermite expansions

  • Published:
Proceedings of the Indian Academy of Sciences - Mathematical Sciences Aims and scope Submit manuscript

Abstract

Regularity properties of twisted spherical means are studied in terms of certain Sobolev spaces defined using Laguerre functions. As an application we prove a localisation theorem for special Hermite expansions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Colzani L, Regularity of spherical means and localisation of spherical harmonic expansions,J. Austr. Math. Soc. 41 (1986) 287–297

    Article  MATH  MathSciNet  Google Scholar 

  2. Folland G, Harmonic analysis in phase space Ann. Math. Stud. (Princeton: University Press) 112 (1989)

    Google Scholar 

  3. Mauceri G, Picardello M and Ricci F, A Hardy space associated with twisted convolution,Adv. Math. 39 (1981) 270–288

    Article  MATH  MathSciNet  Google Scholar 

  4. Oberlin D and Stein E, Mapping properties of the Radon transform,Indiana Univ. Math. J. 31 (1982) 641–650

    Article  MATH  MathSciNet  Google Scholar 

  5. Pinsky M A, Spectral analysis of the Laplacian on piecewise smooth functions (preprint)

  6. Peetre J and Sparr G, Interpolation and non-commutative integration,Ann. Mat. Pura. Appl. Vol. CIV (1975) 187–207

    MathSciNet  Google Scholar 

  7. Peyriere J and Sjolin P, Regularity of spherical means,Ark. Mat. 16 (1978) 177–126

    Article  MathSciNet  Google Scholar 

  8. Sjolin P, Norm inequalities for spherical means,Mh. Math. 100 (1985) 153–161

    Article  MathSciNet  Google Scholar 

  9. Stein E,Singular integrals and differentiability properties of functions (Princeton University Press) (1971)

  10. Stein E, Maximal functions: spherical means,Proc. Natl. Acad. Sci. USA 73 (1976) 2174–2175

    Article  MATH  Google Scholar 

  11. Strichartz R, Harmonic analysis as spectral theory of Laplacians,J. Funct. Anal. 87 (1989) 51–148

    Article  MATH  MathSciNet  Google Scholar 

  12. Szego G, Orthogonal polynomials,Am. Math. Soc. Colloq. Pub., (Providence: Am. Math. Soc.) (1967)

    Google Scholar 

  13. Thangavelu S, On almost everywhere and mean convergence of Hermite and Laguerre expansions,Colloq. Math. 60 (1990) 21–34

    MathSciNet  Google Scholar 

  14. Thangavelu S, Spherical means on the Heisenberg group and a restriction theorem for the symplectic Fourier transform,Revist. Mat. Ibero. (1991) vol.7, No. 2 (1991) 135–155

    MATH  MathSciNet  Google Scholar 

  15. Thangavelu S, On conjugate poisson integrals and Riesz transforms for the Hermite expansions,Colloq. Math. vol.LXIV (1993) 103–113

    MathSciNet  Google Scholar 

  16. Thangavelu S,Lectures on Hermite and Laguerre expansions Math. Notes No. 42 (Princeton: University Press) (to appear)

Download references

Author information

Authors and Affiliations

  1. TIFR Centre, P.B. No. 1234, 560 012, Bangalore, India

    S Thangavelu

Authors
  1. S Thangavelu
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Thangavelu, S. On regularity of twisted spherical means and special Hermite expansions. Proc. Indian Acad. Sci. (Math. Sci.) 103, 303–320 (1993). https://doi.org/10.1007/BF02866993

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02866993

Keywords

Search

Navigation