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Invariant means on double coset spaces


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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  1. N. Bourbaki, Integration. I. Chapters 1–6 (Springer, Berlin, 2004)

    MATH  Google Scholar 

  2. E. Hewitt, K.A. Ross, Abstract Harmonic Analysis, vol. I (Springer, Berlin, 1979)

    MATH  Google Scholar 

  3. G. van Dijk, Introduction to Harmonic Analysis and Generalized Gelfand Pairs (Walter de Gruyter & Co., Berlin, 2009)

    Book  MATH  Google Scholar 

  4. F.P. Greenleaf, Invariant Means on Topological Groups and Their Applications (Van Nostrand Reinhold Co., New York, 1969)

    MATH  Google Scholar 

  5. J. Rosenblatt, Invariant means on the continuous bounded functions. Trans. Am. Math. Soc. 236, 315–324 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  6. J.B. Conway, A Course in Functional Analysis (Springer, New York, 1985)

    Book  MATH  Google Scholar 

  7. J. Dieudonné, Treatise on Analysis, vol. VI (Academic Press Inc, New York, 1978)

    MATH  Google Scholar 

  8. D.H. Hyers, On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27, 222–224 (1941)

    Article  MathSciNet  MATH  Google Scholar 

  9. 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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Correspondence to László Székelyhidi.

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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).

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