Unbounded multipliers and summation of series
نویسندگان
چکیده
منابع مشابه
Summation Notation and Series
Corresponding material in the book: Section 12.1, 12.2, 12.3. What students should definitely get: The summation notation and how it works, series, concepts of convergence. The use of telescoping and forward difference operator ideas to sum up series. The use of the integral test and other tests to determine whether a series converges and obtain numerical estimates. Convergence rules for ration...
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A general summability method of different orthogonal series is given with the help of an integrable function θ. As special cases the trigonometric Fourier, Walsh-, Walsh-Kaczmarz-, Vilenkinand Ciesielski-Fourier series and the Fourier transforms are considered. For each orthonormal system a different Hardy space is introduced and the atomic decomposition of these Hardy spaces are presented. A s...
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A method for analysing a class of divergent series is developed from the Euler– Maclaurin summation formula. The conditions that the summand must satisfy are explored, and a significant simplification is obtained for cases where the summation ranges over all integers. As an example, we consider the Ewald representation for Schlömilch series, and show that this includes Twersky’s dual series for...
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The paper gives a unified treatment of the summation of certain iterated series of the form ∑∞ n=1 ∑∞ m=1 an+m, where (an)n∈N is a sequence of real numbers. We prove that, under certain conditions, the double iterated series equals the difference of two single series.
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1973
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-28-2-287-289