Question

For $\alpha \in \left(0, \frac{1}{2}\right)$, $\sum_{n = 1}^{\infty} \frac{\sin(nx)}{n^{\alpha}}$ is not the Fourier series of a RI-function

score 72 · Answer 1 · 2026-02-24 15:30:40

72

Views

For $\alpha \in \left(0, \frac{1}{2}\right)$, $\sum_{n = 1}^{\infty} \frac{\sin(nx)}{n^{\alpha}}$ is not the Fourier series of a RI-function

Published on 24 Feb 2026 - 15:30

score 52 · Answer 2 · 2026-04-12 08:56:57

52

Views

Sequence definition of continuity for function on $\mathbb R^\mathbb N$

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score 39 · Answer 3 · 2026-04-12 16:53:52

39

Views

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Published on 12 Apr 2026 - 16:53

score 77 · Answer 4 · 2026-04-12 13:51:31

77

Views

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32

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163

Views

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score 39 · Answer 7 · 2026-04-12 03:15:18

39

Views

prove there is no pointwise convergence of $\sin(nx)$

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score 34 · Answer 8 · 2026-02-24 15:25:02

34

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101

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49

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score 41 · Answer 12 · 2026-02-24 15:30:36

41

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score 24 · Answer 13 · 2026-04-11 13:32:41

24

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108

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score 20 · Answer 15 · 2026-04-11 15:35:39

20

Views

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List Question

For $\alpha \in \left(0, \frac{1}{2}\right)$, $\sum_{n = 1}^{\infty} \frac{\sin(nx)}{n^{\alpha}}$ is not the Fourier series of a RI-function

Sequence definition of continuity for function on $\mathbb R^\mathbb N$

Intuition in choosing finite set of points in proof that Pointwise convergence implies convergence in pointwise topology

Summing Over Infinitely Many Frequencies

Convergence almost everywhere criterion

Initial Topology and Weak and Strong Operator Topology

prove there is no pointwise convergence of $\sin(nx)$

Pointwise and uniform convergence for particularly well-behaved functions

Fundamental theorem of $\Gamma$-convergence

Probability convergence of a martingale defined as iid random variable product

Weak Convergence implies Pointwise Convergence (on a Countable set)

If a sequence of finite signed measures converges the sequence of their "maximizers" converges?

Bound for the difference between two functions

Pointwise convergence of generalized inverse function

Applying convergence space to "convergence in measure" and processes

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