Question

Convergence of a complex series on the boundary

score 1k · Answer 1 · 2026-05-06 07:33:59

1k

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Convergence of a complex series on the boundary

Published on 06 May 2026 - 7:33

score 684 · Answer 2 · 2026-05-07 13:41:45

684

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Is there a positive-semidefinite convolution kernel, that is continuous at $0$ but discontinuous elsewhere?

Published on 07 May 2026 - 13:41

score 286 · Answer 3 · 2026-05-06 10:04:01

286

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Extending Lacunary Series beyond their disks

Published on 06 May 2026 - 10:04

score 143 · Answer 4 · 2026-04-22 19:39:34

143

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A tricky limit involving exponential integrals

Published on 22 Apr 2026 - 19:39

score 516 · Answer 5 · 2026-04-29 12:52:37

516

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Continuation of functions beyond natural boundaries

Published on 29 Apr 2026 - 12:52

score 508 · Answer 6 · 2026-04-26 00:50:30

508

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Lacunary Fourier series and Hölder continuity at a point on the circle

Published on 26 Apr 2026 - 0:50

score 294 · Answer 7 · 2026-05-06 10:01:23

294

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If a periodic function with lacunary Fourier series is zero on a small interval then is it smooth?

Published on 06 May 2026 - 10:01

score 20 · Answer 8 · 2026-04-25 04:33:47

20

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Does $\sup_n r_2(E,n)<\infty$ imply $\Lambda(4)$?

Published on 25 Apr 2026 - 4:33

score 312 · Answer 9 · 2026-05-06 10:03:48

312

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Lacunary series - Finding a limit

Published on 06 May 2026 - 10:03

score 138 · Answer 10 · 2026-04-25 02:06:04

138

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$\lim_{x\to 1^-} \sum_{k=0}^\infty \left( x^{k^2}-x^{(k+\alpha)^2}\right)$

Published on 25 Apr 2026 - 2:06

score 146 · Answer 11 · 2026-05-06 10:02:45

146

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How fast does $\lim_{x\to 1^-} \sum_{k=0}^\infty \left( x^{k^2}-x^{(k+\alpha)^2}\right)$ go to $\alpha$?

Published on 06 May 2026 - 10:02

score 53 · Answer 12 · 2026-05-05 07:28:00

53

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Rademacher-like Lacunary Fourier Seires if in $L^2$ then in $L^p$ for $1 \le p < \infty$

Published on 05 May 2026 - 7:28

score 73 · Answer 13 · 2026-04-27 15:57:41

73

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If $\sum_{n\ge0}a_n$ converges, then what is the set $\left\{\sum_{n=0}^\infty\epsilon_n a_n \ : \,\epsilon\in\{0,1\}^\mathbb{N}\right\}$?

Published on 27 Apr 2026 - 15:57

score 52 · Answer 14 · 2026-04-26 22:57:07

52

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For all complex $|z| \neq 1$ : $\sum_{n=0}^{\infty} w_n \frac{z^n}{1+z^n+z^{2n}+z^{3n}+z^{4n}} = \sum_{n=0}^{\infty} u_n \frac{z^n}{1+z^n+z^{2n}}$?

Published on 26 Apr 2026 - 22:57

score 42 · Answer 15 · 2026-05-05 15:19:12

42

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When is $f(z)$ analytic in the neigbourhood of $z$ for some complex $z$ close to the real line?

Published on 05 May 2026 - 15:19

List Question

Convergence of a complex series on the boundary

Is there a positive-semidefinite convolution kernel, that is continuous at $0$ but discontinuous elsewhere?

Extending Lacunary Series beyond their disks

A tricky limit involving exponential integrals

Continuation of functions beyond natural boundaries

Lacunary Fourier series and Hölder continuity at a point on the circle

If a periodic function with lacunary Fourier series is zero on a small interval then is it smooth?

Does $\sup_n r_2(E,n)<\infty$ imply $\Lambda(4)$?

Lacunary series - Finding a limit

$\lim_{x\to 1^-} \sum_{k=0}^\infty \left( x^{k^2}-x^{(k+\alpha)^2}\right)$

How fast does $\lim_{x\to 1^-} \sum_{k=0}^\infty \left( x^{k^2}-x^{(k+\alpha)^2}\right)$ go to $\alpha$?

Rademacher-like Lacunary Fourier Seires if in $L^2$ then in $L^p$ for $1 \le p < \infty$

If $\sum_{n\ge0}a_n$ converges, then what is the set $\left\{\sum_{n=0}^\infty\epsilon_n a_n \ : \,\epsilon\in\{0,1\}^\mathbb{N}\right\}$?

For all complex $|z| \neq 1$ : $\sum_{n=0}^{\infty} w_n \frac{z^n}{1+z^n+z^{2n}+z^{3n}+z^{4n}} = \sum_{n=0}^{\infty} u_n \frac{z^n}{1+z^n+z^{2n}}$?

When is $f(z)$ analytic in the neigbourhood of $z$ for some complex $z$ close to the real line?

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