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1997 | 126 | 1 | 1-12
Tytuł artykułu

A restriction theorem for the Heisenberg motion

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove a restriction theorem for the class-1 representations of the Heisenberg motion group. This is done using an improvement of the restriction theorem for the special Hermite projection operators proved in [13]. We also prove a restriction theorem for the Heisenberg group.
Czasopismo
Rocznik
Tom
126
Numer
1
Strony
1-12
Opis fizyczny
Daty
wydano
1997
otrzymano
1995-10-05
poprawiono
1997-06-10
Twórcy
  • Statistics and Mathematics unit, Indian Statistical Institute, 8th mile, Mysore Road, Bangalore 560 059, India , ratna@isibang.ernet.in
autor
  • Statistics and Mathematics unit, Indian Statistical Institute, 8th mile, Mysore Road, Bangalore 560 059, India , rawat@isibang.ernet.in
  • Statistics and Mathematics unit, Indian Statistical Institute, 8th mile, Mysore Road, Bangalore 560 059, India , veluma@isibang.ernet.in
Bibliografia
  • [1] G. B. Folland, Harmonic Analysis in Phase Space, Ann. of Math. Stud. 122, Princeton Univ. Press, Princeton, N.J., 1989.
  • [2] R. Gangolli, Spherical functions on semisimple Lie groups, in: Symmetric Spaces, W. Boothby and G. Weiss (eds.), Dekker, New York, 1972, 41-92.
  • [3] A. Hulanicki and F. Ricci, A Tauberian theorem and tangential convergence for bounded harmonic functions on balls in $ℂ^n$, Invent. Math. 62 (1980), 325-331.
  • [4] C. Markett, Mean Cesàro summability of Laguerre expansions and norm estimates with shifted parameter, Anal. Math. 8 (1982), 19-37.
  • [5] D. Müller, A restriction theorem for the Heisenberg group, Ann. of Math. 131 (1990), 567-587.
  • [6] D. Müller, On Riesz means of eigenfunction expansions for the Kohn-Laplacian, J. Reine Angew. Math. 401 (1989), 113-121.
  • [7] J. Peetre and G. Sparr, Interpolation and non-commutative integration, Ann. Mat. Pura Appl. 104 (1975), 187-207.
  • [8] R. Rawat, A theorem of the Wiener-Tauberian type for $L^1(H^n)$, Proc. Indian Acad. Sci. Math. Sci. 106 (1996), 369-377.
  • [9] C. Sogge, Oscillatory integrals and spherical harmonics, Duke Math. J. 53 (1986), 43-65.
  • [10] C. Sogge, Concerning the $L^p$ norm of spectral clusters for second-order elliptic operators on compact manifolds, J. Funct. Anal. 77 (1988), 123-134.
  • [11] E. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, Princeton, N.J., 1993.
  • [12] R. Strichartz, $L^p$ harmonic analysis and Radon transforms on the Heisenberg group, J. Funct. Anal. 96 (1991), 350-406.
  • [13] S. Thangavelu, Weyl multipliers, Bochner-Riesz means and special Hermite expansions, Ark. Mat. 29 (1991), 307-321.
  • [14] S. Thangavelu, Restriction theorems for the Heisenberg group, J. Reine Angew. Math. 414 (1991), 51-65.
  • [15] S. Thangavelu, Some restriction theorems for the Heisenberg group, Studia Math. 99 (1991), 11-21.
  • [16] S. Thangavelu, Lectures on Hermite and Laguerre Expansions, Math. Notes 42, Princeton Univ. Press, Princeton, N.J., 1993.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv126i1p1bwm
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