Bondioli, Cristiana:
Un teorema di Paley-Wiener per funzioni ultradifferenziabili su uno spazio simmetrico
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Serie 8 73 (1982), fasc. n.5, p. 89-96, (Italian)
pdf (417 Kb), djvu (335 Kb). | MR 0726285
Sunto
We prove a Paley-Wiener theorem for ultradifferentiable functions of class $M_{p}$ on a symmetric space of the non compact type and arbitrary rank.
Referenze Bibliografiche
[1] J. Faraut (1980) - Analyse harmonique sur les espaces riemanniens symétriques de rang un, CIMPA, Université de Nancy I.
[2] J. Faraut (1981) - Un théorème de Paley-Wiener pour la transformation de Fourier sur un espace riemannien symétrique de rang un, (preprint).
[3]
R. Gangolli (
1971) -
On the Plancherel formula and the Paley-Wiener theorem for spherical functions on semisimple Lie groups,
«Ann. of Math.»,
93, 150-165. |
MR 289724 |
Zbl 0232.43007[4]
Harish-Chandra (
1958) -
Spherical functions on a semisimple Lie group, I, II,
«Amer. J. Math.»,
80, 241-310, 553-613. |
MR 94407 |
Zbl 0093.12801[5]
S. Helgason (
1962) -
Differential Geometry and Symmetric Spaces,
Academic Press, New York. |
MR 145455[6]
S. Helgason (
1964) -
Fundamental solutions of invariant differential operators on symmetric spaces,
«Amer, J. Math.»,
86, 565-601. |
MR 165032 |
Zbl 0178.17001[7]
S. Helgason (
1968) -
Lie groups and symmetric spaces, in
«Battelle Rencontres 1967»,
W.A. Benjamin, Inc., New York, pp. 1—71. |
MR 236325 |
Zbl 0177.50601[8]
S. Helgason (
1970) -
A duality for symmetric spaces, with applications to group representations,
«Advan. Math.»,
5, 1-154. |
MR 263988 |
Zbl 0209.25403[9]
S. Helgason (
1973) -
The surjectivity of invariant differential operators on symmetric spaces,
«Ann. of Math.», (2)
98, 451-479. |
MR 367562 |
Zbl 0274.43013[10]
H. Komatsu (
1973) -
Ultradistributions, I, Structure theorems and a characterization,
«J. Fac. Sci. Univ. Tokyo», Sec. IA,
20, 25-105. |
MR 320743 |
Zbl 0258.46039[11]
J.B. Lewis (
1978) -
Eigenfunctions on symmetric spaces with distribution-valued boundary forms,
«J. Functional Analysis»,
29, 287-307. |
fulltext (doi) |
MR 512246 |
Zbl 0398.43010[12]
J.L. Lions e
E. Magenes (
1973) -
Non-Homogeneous Boundary Value Problems and Applications, Vol.
III,
Springer-Verlag, Berlin-Heidelberg-New York. |
MR 350179[13]
S. Mandelbrojt (
1952) -
Séries adhérentes, régularisations des suites. Applications,
Gauthier-Villars, Paris. |
MR 51893[14]
C. Roumieu (
1960) -
Sur quelques extensions de la notion de distribution,
«Ann. Scient. Ec. Norm. Sup.»,
77, 47-121. |
fulltext EuDML |
MR 121643[15]
C. Roumieu (
1962) -
Ultradistributions définies sur $\mathbf{R}^{n}$ et sur certaines classes de variétés différentiables,
«J. Analyse Math.»,
10, 153-192. |
MR 158261 |
Zbl 0122.34802
Con il contributo del Ministero per i Beni e le Attività Culturali