Spectral synthesis on symmetric spaces. (English) Zbl 0613.53030
Integral geometry, Proc. AMS-IMS-SIAM Joint Summer Res. Conf., Brunswick/Maine 1984, Contemp. Math. 63, 1-25 (1987).
[For the entire collection see Zbl 0602.00005.]
The paper contains an overview (up to the time of the conference) of the Pompeiu problem and the spectral synthesis problem in \(C^{\infty}(X)\), X being a symmetric space of the non-compact type. The more recent results of the author with R. Gay on the local Pompeiu problem [Isr. J. Math. 55, 267-288 (1986)] might indicate a new way to consider the open problems mentioned in this paper.
The paper contains an overview (up to the time of the conference) of the Pompeiu problem and the spectral synthesis problem in \(C^{\infty}(X)\), X being a symmetric space of the non-compact type. The more recent results of the author with R. Gay on the local Pompeiu problem [Isr. J. Math. 55, 267-288 (1986)] might indicate a new way to consider the open problems mentioned in this paper.
MSC:
| 53C65 | Integral geometry |
| 43A85 | Harmonic analysis on homogeneous spaces |
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
| 53C35 | Differential geometry of symmetric spaces |
| 22E46 | Semisimple Lie groups and their representations |
