Two-radii theorems for quasi-analytic classes of functions on a sphere

被引：0
作者：
Volchkov V.V. [1 ]
Volchkov V.V. [1 ]
机构：
[1] Donetsk National University, Donetsk, 83001, 24, Universitetskaya Str.
来源：
Journal of Mathematical Sciences | 2013年 / 194卷 / 5期
关键词：
Legendre functions; quasianalyticity; spherical harmonics; spherical means; spherical transformation;
D O I：
10.1007/s10958-013-1548-6
中图分类号：
学科分类号：
摘要：
The problem of existence of non-trivial functions in quasi-analytic classes on a sphere that have zero integrals over all balls centered on a given set is investigated. The case where the set of centers is the union of two concentric spheres is completely studied. © 2013 Springer Science+Business Media New York.
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页码：584 / 602
页数：18
相关论文
共 24 条
  • [1] Agranovsky M.L., Volchkov V.V., Zalcman L.A., Conical injectivity sets for the spherical Radon transform, Bull. London Math. Soc., 31, pp. 231-236, (1999)
  • [2] Badertscher E., The Pompeiu problem on locally symmetric spaces, J. D'analyse Math., 57, pp. 250-281, (1991)
  • [3] Bateman H., Erdelyi A., Higher Transcendental Functions, 1-3, (1953)
  • [4] Berenstein C.A., Gay R., A local version of the two-circles theorem, Israel J. Math., 55, pp. 267-288, (1986)
  • [5] Berenstein C.A., Zalcman L., Pompeiu's problem on spaces of constant curvature, J. Analyse Math., 30, pp. 113-130, (1976)
  • [6] Berenstein C.A., Zalcman L., Pompeiu's problem on symmetric spaces, Comment. Math. Helv., 55, pp. 593-621, (1980)
  • [7] Brown L., Schreiber B.M., Taylor B.A., Spectral synthesis and the Pompeiu problem, Ann. Inst. Fourier, Grenoble, 23, 3, pp. 125-154, (1973)
  • [8] Helgason S., Groups and Geometric Analysis, (1984)
  • [9] Hormander L., The Analysis of Linear Partial Differential Operators, 2, (1983)
  • [10] Kolmogorov A.N., Fomin S.V., Elements of the Theory of Functions and Functional Analysis, (1999)
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