Her 1953 paper established several important results on summability kernels and is referenced in two textbooks on functional analysis.
12.
In physics, there are a wide variety of summability methods; these are discussed in greater detail in the article on regularization.
13.
In the 1950s, he laid the basis on systematic treatment of summability factors together with German mathematicians Alexander Peyerimhoff and Wolfgang Jurkat.
14.
The lack of convergence of the Fourier series has led to the introduction of a variety of summability methods in order to produce convergence.
15.
Then, provided that " f " obeys certain summability conditions, then it may be represented in terms of these polynomials as
16.
One of her most popular theorems called the Norlund Mean can be explained through absolute regularity, the summability of Cauchy products, and inverse properties.
17.
As shown above, holds under the much less restrictive assumption that " s " ( " t " ) is in Ces�ro summability.
18.
With the result of the previous section, this implies an equivalence between summability of and with methods that are linear, stable, and respect the Cauchy product.
19.
The Silverman Toeplitz theorem characterizes " matrix summability methods ", which are methods for summing a divergent series by applying an infinite matrix to the vector of coefficients.
20.
When " S " = "'N "'is the set of natural numbers, Lebesgue integrability, unordered summability and absolute convergence all coincide.
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