Question

If $r_n\to r$ and $s_n\to s$, then $(r \star s)_M/M \to rs$.

score 62 · Answer 1 · 2014-04-18 03:19:40

62

Views

If $r_n\to r$ and $s_n\to s$, then $(r \star s)_M/M \to rs$.

Published on 18 Apr 2014 - 3:19

score 447 · Answer 2 · 2014-06-25 10:12:11

447

Views

Cesaro summability together with $\lim nu_n\to 0$ implies convergence

Published on 25 Jun 2014 - 10:12

score 779 · Answer 3 · 2014-08-27 01:58:09

779

Views

Does $\sum_{i=1}^\infty a_i/i < \infty$ imply that $a_i$ has Cesaro mean zero?

Published on 27 Aug 2014 - 1:58

score 131 · Answer 4 · 2014-09-05 09:46:01

131

Views

Show that for a sequence of real numbers $(a_n)_n$ $\lim_n a_n=0$ implies $\frac{1}{n}\sum_{i=0}^{n-1}\lvert a_i\rvert=0$

Published on 05 Sep 2014 - 9:46

score 880 · Answer 5 · 2014-09-14 02:31:51

880

Views

A result on sequences: $x_n\to x$ implies $\frac{x_1+\dots+x_n}n\to x$ without using Stolz-Cesaro

Published on 14 Sep 2014 - 2:31

score 522 · Answer 6 · 2014-10-09 20:00:36

522

Views

Cesàro summability and $\sum n \lvert a_n\rvert ^2 < \infty$ implies convergence

Published on 09 Oct 2014 - 20:00

score 1k · Answer 7 · 2014-10-14 02:56:00

1k

Views

Cesàro summability implies convergence of (conventional) sum when $\sum_{n=1}^\infty na_n^2<\infty$

Published on 14 Oct 2014 - 2:56

score 92 · Answer 8 · 2014-11-03 05:07:48

92

Views

$\frac{a_n - a_{n+1}}{a_n} \approx \frac{1}{n}$? (part of 2010 Putnam exam)

Published on 03 Nov 2014 - 5:07

score 1k · Answer 9 · 2014-11-28 23:00:10

1k

Views

Cesàro summable sequences

Published on 28 Nov 2014 - 23:00

score 200 · Answer 10 · 2014-12-08 22:53:17

200

Views

asymptotics of sum

Published on 08 Dec 2014 - 22:53

score 1.3k · Answer 11 · 2014-12-09 13:14:57

1.3k

Views

Cesáro sums and the actual limit

Published on 09 Dec 2014 - 13:14

score 69 · Answer 12 · 2019-10-27 20:26:31

69

Views

If I know the limit of Cesaro averages , then can I know limits of uniform Cesaro averages. Details Below

Published on 27 Oct 2019 - 20:26

score 133 · Answer 13 · 2019-12-04 23:05:39

133

Views

Proof of the integral representation of the arithmetic mean of the partial sums of Fourier series

Published on 04 Dec 2019 - 23:05

score 193 · Answer 14 · 2026-02-23 01:30:46

193

Views

Convergence of Cesaro sums on $L^p$

Published on 23 Feb 2026 - 1:30

score 85 · Answer 15 · 2020-02-21 15:58:25

85

Views

Unbounded series with finite Cesàro mean

Published on 21 Feb 2020 - 15:58

List Question

If $r_n\to r$ and $s_n\to s$, then $(r \star s)_M/M \to rs$.

Cesaro summability together with $\lim nu_n\to 0$ implies convergence

Does $\sum_{i=1}^\infty a_i/i < \infty$ imply that $a_i$ has Cesaro mean zero?

Show that for a sequence of real numbers $(a_n)_n$ $\lim_n a_n=0$ implies $\frac{1}{n}\sum_{i=0}^{n-1}\lvert a_i\rvert=0$

A result on sequences: $x_n\to x$ implies $\frac{x_1+\dots+x_n}n\to x$ without using Stolz-Cesaro

Cesàro summability and $\sum n \lvert a_n\rvert ^2 < \infty$ implies convergence

Cesàro summability implies convergence of (conventional) sum when $\sum_{n=1}^\infty na_n^2<\infty$

$\frac{a_n - a_{n+1}}{a_n} \approx \frac{1}{n}$? (part of 2010 Putnam exam)

Cesàro summable sequences

asymptotics of sum

Cesáro sums and the actual limit

If I know the limit of Cesaro averages , then can I know limits of uniform Cesaro averages. Details Below

Proof of the integral representation of the arithmetic mean of the partial sums of Fourier series

Convergence of Cesaro sums on $L^p$

Unbounded series with finite Cesàro mean

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