Question

Convergence of a complex series on the boundary

score 1k · Answer 1 · 2026-03-19 17:14:21

1k

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Convergence of a complex series on the boundary

Published on 19 Mar 2026 - 17:14

score 678 · Answer 2 · 2026-03-25 01:03:32

678

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

Published on 25 Mar 2026 - 1:03

score 280 · Answer 3 · 2026-03-19 21:09:36

280

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Extending Lacunary Series beyond their disks

Published on 19 Mar 2026 - 21:09

score 139 · Answer 4 · 2026-03-22 08:13:06

139

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A tricky limit involving exponential integrals

Published on 22 Mar 2026 - 8:13

score 508 · Answer 5 · 2026-03-22 12:33:28

508

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Continuation of functions beyond natural boundaries

Published on 22 Mar 2026 - 12:33

score 503 · Answer 6 · 2026-03-19 23:16:06

503

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

Published on 19 Mar 2026 - 23:16

score 288 · Answer 7 · 2026-03-19 13:32:19

288

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

Published on 19 Mar 2026 - 13:32

score 16 · Answer 8 · 2026-03-19 15:33:57

16

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

Published on 19 Mar 2026 - 15:33

score 305 · Answer 9 · 2026-03-19 16:06:13

305

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Lacunary series - Finding a limit

Published on 19 Mar 2026 - 16:06

score 133 · Answer 10 · 2026-03-19 14:24:01

133

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

Published on 19 Mar 2026 - 14:24

score 140 · Answer 11 · 2026-03-19 20:01:01

140

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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 19 Mar 2026 - 20:01

score 47 · Answer 12 · 2026-03-16 18:48:54

47

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

Published on 16 Mar 2026 - 18:48

score 68 · Answer 13 · 2026-03-17 00:12:05

68

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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 17 Mar 2026 - 0:12

score 46 · Answer 14 · 2026-03-16 15:40:03

46

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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 16 Mar 2026 - 15:40

score 35 · Answer 15 · 2026-03-16 19:07:43

35

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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 16 Mar 2026 - 19:07

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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