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1999 | 80 | 2 | 211-233
Tytuł artykułu

A Paley-Wiener theorem on NA harmonic spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let N be an H-type group and consider its one-dimensional solvable extension NA, equipped with a suitable left-invariant Riemannian metric. We prove a Paley-Wiener theorem for nonradial functions on NA supported in a set whose boundary is a horocycle of the form Na, a ∈ A.
Słowa kluczowe
Rocznik
Tom
80
Numer
2
Strony
211-233
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-02-24
poprawiono
1998-10-16
Twórcy
  • Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
  • Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
Bibliografia
  • [ADY] J.-P. Anker, E. Damek and C. Yacoub, Spherical analysis on harmonic AN groups, Ann. Scuola Norm. Sup. Pisa 33 (1996), 643-679.
  • [ACD] F. Astengo, R. Camporesi and B. Di Blasio, The Helgason Fourier transform on a class of nonsymmetric harmonic spaces, Bull. Austral. Math. Soc. 55 (1997), 405-424.
  • M. Cowling, A. H. Dooley, A. Korányi and F. Ricci, An approach to symmetric spaces of rank one via groups of Heisenberg type, J. Geom. Anal., to appear.
  • [CH] M. G. Cowling and U. Haagerup, Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one, Invent. Math. 96 (1989), 507-549.
  • [Da1] E. Damek, A Poisson kernel on Heisenberg type nilpotent groups, Colloq. Math. 53 (1987), 239-247.
  • [Da2] E. Damek, Curvature of a semidirect extension of a Heisenberg type nilpotent group, ibid., 249-253.
  • [Da3] E. Damek, Geometry of a semidirect extension of a Heisenberg type nilpotent group, ibid., 255-268.
  • E. Damek and F. Ricci, Harmonic analysis on solvable extensions of H-type groups, J. Geom. Anal. 2 (1992), 213-248.
  • E. Damek and F. Ricci, A class of nonsymmetric harmonic Riemannian spaces, Bull. Amer. Math. Soc. 27 (1992), 139-142.
  • [Di] B. Di Blasio, Paley-Wiener type theorems on harmonic extensions of H-type groups, Monatsh. Math. 123 (1997), 21-42.
  • [DoZ] A. Dooley and G. Zhang, Spherical functions on H-type groups, preprint.
  • [EbO] P. Eberlein and B. O'Neill, Visibility manifolds, Pacific J. Math. 46 (1973), 45-109.
  • A. Erdélyi, W. Magnus, F. Oberhettinger and G. Tricomi, Higher Transcendental Functions, Vols. I, II, McGraw-Hill, New York, 1953.
  • [F] J. Faraut, Un théorème de Paley-Wiener pour la transformation de Fourier sur un espace riemannien symétrique de rang un, J. Funct. Anal. 49 (1982), 230-268.
  • [GV] R. Gangolli and V. S. Varadarajan, Harmonic Analysis of Spherical Functions on Real Reductive Groups, Ergeb. Math. Grenzgeb. 101, Springer, Berlin and New York, 1988.
  • [HC] Harish-Chandra, Discrete series for semisimple Lie groups, Acta Math. 116 (1966), 1-111.
  • [He] S. Helgason, Geometric Analysis on Symmetric Spaces, Math. Surveys Monographs 39, Amer. Math. Soc., Providence, R.I., 1994.
  • [H] A. Hulanicki, Subalgebra of $L_1(G)$ associated with laplacian on a Lie group, Colloq. Math. 31 (1974), 259-287.
  • [HR] 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.
  • [Ka1] A. Kaplan, Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms, Trans. Amer. Math. Soc. 258 (1980), 147-153.
  • [Ka2] A. Kaplan, Riemannian nilmanifolds attached to Clifford modules, Geom. Dedicata 11 (1981), 127-136.
  • [Ko1] A. Korányi, Some applications of Gelfand pairs in classical analysis, in: Harmonic Analysis and Group Representations, C.I.M.E., Liguori, Napoli, 1980, 333-348.
  • [Ko2] A. Korányi, Geometric properties of Heisenberg type groups, Adv. Math. 56 (1985), 28-38.
  • [Ri1] F. Ricci, Harmonic analysis on groups of type H, preprint.
  • [Ri2] F. Ricci, The spherical transform on harmonic extensions of H-type groups, Rend. Sem. Mat. Univ. Politec. Torino 50 (1992), 381-392.
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  • [V] V. S. Varadarajan, Harmonic Analysis on Real Reductive Groups, Lecture Notes in Math. 576, Springer, Berlin, 1977.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv80i2p211bwm
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