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Volume 11 - Issue 2 - June 1968

Contents

Page 2 of 5

Research Article

  • A Genuine Topology for the Field of Mikusiński Operators

  • Raimond A. Struble
  • Published online by Cambridge University Press:
    20 November 2018, pp. 297-299
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  • Let C denote the complex algebra of continuous functions of a non-negative real variable under addition, scalar multiplication and convolution. C has no divisors of zero and its quotient field F is called the field of Mikusiński operators [1]. It is well known that Mikusiński has defined a sequential convergence in F which is not topological [2]. Using a recent result due to T.K. Boehem [3] we shall provide F with a sequential convergence which is topological.

Book Reviews: Comptes Rendus Critiques

  • A graduate course in probability, by Howard G. Tucker. Academic Press, New York and London, 1967. xiii + 273 pages. $14.00.

  • D.A. Dawson
  • Published online by Cambridge University Press:
    01 April 2019, pp. 326-327
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  • Polish logic, 1920-1939, edited by Storrs McCall. Oxford University Press, 1967. viii + 406 pages. $15.00.

  • J. Lambek
  • Published online by Cambridge University Press:
    01 April 2019, p. 346
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  • Foundations of the calculus, by H. F. DeBaggis and K.S. Miller. Saunders, 1966. $5.00.

  • H. A. Thurston
  • Published online by Cambridge University Press:
    01 April 2019, pp. 330-331
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  • A first course in Stochastic Processes, by Samuel Karlin. Academic Press N.Y. and London 502 pages. $11.95.

  • Charles Kraft
  • Published online by Cambridge University Press:
    01 April 2019, p. 317
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  • A selection of early statistical papers of J. Neyman. University of California Press, 1967. ix + 429 pages. $14.95.

  • C. Kraft
  • Published online by Cambridge University Press:
    01 April 2019, pp. 340-341
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  • Ring and radicals, by N. J. Divinsky. University of Toronto. $7.50.

  • S.A. Amitsur
  • Published online by Cambridge University Press:
    01 April 2019, pp. 320-323
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  • Abstract Algebra, by CrH. Sah. Academic Press, New York and London, 1967. xiii + 352 pages. $9.75.

  • John D. Dixon
  • Published online by Cambridge University Press:
    01 April 2019, pp. 311-312
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  • Theory of Rank Tests, by J. Hajek and Z. Sidak. Academic Press, 1967. 297 pages. $8.00.

  • C. Kraft
  • Published online by Cambridge University Press:
    01 April 2019, p. 340
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Books Received

  • Books Received

  • Published online by Cambridge University Press:
    01 April 2019, pp. 361-364
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Other

  • Solutions

  • Published online by Cambridge University Press:
    01 April 2019, pp. 306-309
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Research Article

  • A Remark on the Gibbs Phenomenon and Lebesgue Constants for a Summability Method of Melikov

  • Fred Ustina
  • Published online by Cambridge University Press:
    20 November 2018, pp. 301-303
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  • Let u = ∑uk be a given series and let Melikov [4] has defined the n-th σ- transform of u by

    where ε and θ are assumed to be non-negative. This is easily shown to be equivalent to

    The method is a generalization of a method used by Kaufman [l], and of another one used by Melikov [5]. It reduces to the (n-l)th (C;l) mean when θ = 0 and ε = 0, and to the n-th (C;l) mean when θ = 1 and ε = 0.

Book Reviews: Comptes Rendus Critiques

Page 2 of 5