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.
@article{bwmeta1.element.bwnjournal-article-smv126i1p1bwm, author = {P. Ratnakumar and Rama Rawat and S. Thangavelu}, title = {A restriction theorem for the Heisenberg motion}, journal = {Studia Mathematica}, volume = {122}, year = {1997}, pages = {1-12}, zbl = {0978.42016}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv126i1p1bwm} }
Ratnakumar, P.; Rawat, Rama; Thangavelu, S. A restriction theorem for the Heisenberg motion. Studia Mathematica, Tome 122 (1997) pp. 1-12. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv126i1p1bwm/
[00000] [1] G. B. Folland, Harmonic Analysis in Phase Space, Ann. of Math. Stud. 122, Princeton Univ. Press, Princeton, N.J., 1989. | Zbl 0682.43001
[00001] [2] R. Gangolli, Spherical functions on semisimple Lie groups, in: Symmetric Spaces, W. Boothby and G. Weiss (eds.), Dekker, New York, 1972, 41-92. | Zbl 0252.43026
[00002] [3] A. Hulanicki and F. Ricci, A Tauberian theorem and tangential convergence for bounded harmonic functions on balls in , Invent. Math. 62 (1980), 325-331. | Zbl 0449.31008
[00003] [4] C. Markett, Mean Cesàro summability of Laguerre expansions and norm estimates with shifted parameter, Anal. Math. 8 (1982), 19-37. | Zbl 0515.42023
[00004] [5] D. Müller, A restriction theorem for the Heisenberg group, Ann. of Math. 131 (1990), 567-587. | Zbl 0731.43003
[00005] [6] D. Müller, On Riesz means of eigenfunction expansions for the Kohn-Laplacian, J. Reine Angew. Math. 401 (1989), 113-121. | Zbl 0697.35102
[00006] [7] J. Peetre and G. Sparr, Interpolation and non-commutative integration, Ann. Mat. Pura Appl. 104 (1975), 187-207. | Zbl 0309.46031
[00007] [8] R. Rawat, A theorem of the Wiener-Tauberian type for , Proc. Indian Acad. Sci. Math. Sci. 106 (1996), 369-377.
[00008] [9] C. Sogge, Oscillatory integrals and spherical harmonics, Duke Math. J. 53 (1986), 43-65.
[00009] [10] C. Sogge, Concerning the norm of spectral clusters for second-order elliptic operators on compact manifolds, J. Funct. Anal. 77 (1988), 123-134. | Zbl 0641.46011
[00010] [11] E. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Univ. Press, Princeton, N.J., 1993. | Zbl 0821.42001
[00011] [12] R. Strichartz, harmonic analysis and Radon transforms on the Heisenberg group, J. Funct. Anal. 96 (1991), 350-406. | Zbl 0734.43004
[00012] [13] S. Thangavelu, Weyl multipliers, Bochner-Riesz means and special Hermite expansions, Ark. Mat. 29 (1991), 307-321. | Zbl 0765.42009
[00013] [14] S. Thangavelu, Restriction theorems for the Heisenberg group, J. Reine Angew. Math. 414 (1991), 51-65. | Zbl 0708.43003
[00014] [15] S. Thangavelu, Some restriction theorems for the Heisenberg group, Studia Math. 99 (1991), 11-21. | Zbl 0747.43003
[00015] [16] S. Thangavelu, Lectures on Hermite and Laguerre Expansions, Math. Notes 42, Princeton Univ. Press, Princeton, N.J., 1993.