Abstract
In this paper we study invariant means on and amenability of double coset spaces. We prove the amenability of Gelfand pairs. As an application we prove a stability theorem for a functional equation related to spherical functions.
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References
N. Bourbaki, Integration. I. Chapters 1–6 (Springer, Berlin, 2004)
E. Hewitt, K.A. Ross, Abstract Harmonic Analysis, vol. I (Springer, Berlin, 1979)
G. van Dijk, Introduction to Harmonic Analysis and Generalized Gelfand Pairs (Walter de Gruyter & Co., Berlin, 2009)
F.P. Greenleaf, Invariant Means on Topological Groups and Their Applications (Van Nostrand Reinhold Co., New York, 1969)
J. Rosenblatt, Invariant means on the continuous bounded functions. Trans. Am. Math. Soc. 236, 315–324 (1978)
J.B. Conway, A Course in Functional Analysis (Springer, New York, 1985)
J. Dieudonné, Treatise on Analysis, vol. VI (Academic Press Inc, New York, 1978)
D.H. Hyers, On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27, 222–224 (1941)
L. Székelyhidi, Remark 17. In Report of Meeting: The Twenty-second International Symposium on Functional Equations, December 16–December 22, 1984, Oberwolfach, Germany. Aequa. Math. 29(1), 62–111 (1985)
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The research was supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. K111651.
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Székelyhidi, L. Invariant means on double coset spaces. Period Math Hung 75, 58–65 (2017). https://doi.org/10.1007/s10998-017-0196-x
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DOI: https://doi.org/10.1007/s10998-017-0196-x