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2 results

  • 11 - Summability

  • from Part III - Discrete Functional Analysis
  • Martin Buntinas, Loyola University, Chicago
  • Book:
    Classical and Discrete Functional Analysis with Measure Theory
    Published online:
    06 January 2022
    Print publication:
    20 January 2022, pp 440-448

  • Summary

    Summability Theory deals with the assignment a sum to a divergent series or a limit to a divergent sequence. The basics of Summability Theory are given in this chapter. Cesaro Summability is studied in some detail. It is an example of a Matrix Summability Method. The Silverman–Toeplitz Theorem, which characterizes Matrix Summability Methods that sum all convergent series, is proven. Also, the Abel Summability Method, which is not a Matrix Summability Method, is studied.

  • On the support of tempered distributions

  • Part of
  • Jasson Vindas, Ricardo Estrada
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 53 / Issue 1 / February 2010
    Published online by Cambridge University Press:
    12 January 2010, pp. 255-270
    • Article
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  • We show that if the summability means in the Fourier inversion formula for a tempered distribution f ∈ S′(ℝn) converge to zero pointwise in an open set Ω, and if those means are locally bounded in L1(Ω), then Ω ⊂ ℝn\supp f. We prove this for several summability procedures, in particular for Abel summability, Cesàro summability and Gauss-Weierstrass summability.