List questions from summability-theory

Published on 20 Mar 2026 - 3:14

67

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Continuation beyond the natural boundary with $f_+(z)=\lim_{x \to 1-} f(z,x)=\lim_{x \to 1-}\sum_{n=1}^{\infty}\frac{z^{n^2}}{n^n}n^{-n^2 (1-x)} x^n$

Published on 19 Mar 2026 - 6:15

551

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Where to find a proof of Silverman-Toeplitz?

Published on 13 Oct 2013 - 1:04

124

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Is the series corresponding to a summable family absolutely convergent?

Published on 19 Mar 2026 - 5:21

90

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If $E$ is a normed $ℝ$-vector space, are we able to show that $(x_i)_{i∈I}⊆E$ is summable $⇔$ $\left(\left\|x_i\right\|_E\right)_{i∈I}$ is summable?

Published on 01 Jun 2017 - 13:23

774

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Proof Silverman-Toeplitz theorem

Published on 24 Aug 2017 - 17:59

704

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A Summability methods which sum the harmonic series

Published on 23 Sep 2017 - 11:29

279

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An oscillating series of real numbers which can be resummed to a complex value

Published on 10 Oct 2017 - 20:31

203

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Integrability with respect to counting measure

Published on 03 Oct 2020 - 22:14

67

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If $\mu$ is a finite measure on a metric space, then for all $\varepsilon$, there is a $\delta<\delta$ with $\mu(\partial B_\delta(x))=0$

Published on 20 Dec 2020 - 20:24

63

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Generalizing Borel Summation to Matrices

Published on 29 Jun 2021 - 7:04

318

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Product of two locally integrable function is locally integrable?

Published on 23 Sep 2021 - 9:15

124

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A question on summable families in topological groups

Published on 10 Dec 2021 - 16:33

List Question

Are the sequences of families for summability or improper summability:

Continuation beyond the natural boundary with $f_+(z)=\lim_{x \to 1-} f(z,x)=\lim_{x \to 1-}\sum_{n=1}^{\infty}\frac{z^{n^2}}{n^n}n^{-n^2 (1-x)} x^n$

Where to find a proof of Silverman-Toeplitz?

Is the series corresponding to a summable family absolutely convergent?

If $E$ is a normed $ℝ$-vector space, are we able to show that $(x_i)_{i∈I}⊆E$ is summable $⇔$ $\left(\left\|x_i\right\|_E\right)_{i∈I}$ is summable?

Proof Silverman-Toeplitz theorem

A Summability methods which sum the harmonic series

An oscillating series of real numbers which can be resummed to a complex value

Integrability with respect to counting measure

If $\mu$ is a finite measure on a metric space, then for all $\varepsilon$, there is a $\delta<\delta$ with $\mu(\partial B_\delta(x))=0$

Generalizing Borel Summation to Matrices

Product of two locally integrable function is locally integrable?

A question on summable families in topological groups

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