Question

If $f \in L^p(\Bbb R)$ for $1 < p\le 2$, then $f\ast \frac{\sin \pi t}{\pi t} \in L^p(\Bbb R)$.

score 99 · Answer 1 · 2026-04-15 19:44:32

99

Views

If $f \in L^p(\Bbb R)$ for $1 < p\le 2$, then $f\ast \frac{\sin \pi t}{\pi t} \in L^p(\Bbb R)$.

Published on 15 Apr 2026 - 19:44

score 98 · Answer 2 · 2026-04-15 18:05:38

98

Views

Find $\min \sum |a_n|$ when $\sum |a_n|^2 = 1$ and $\sum |a_n|^4 = \lambda$ (Katznelson's Ex $4.1.2.$)

Published on 15 Apr 2026 - 18:05

score 19 · Answer 3 · 2026-04-11 08:23:42

19

Views

Identify Closed Subgroup in Compact Abelian Group

Published on 11 Apr 2026 - 8:23

score 45 · Answer 4 · 2026-04-17 08:05:33

45

Views

Error with Fourier Transform

Published on 17 Apr 2026 - 8:05

score 36 · Answer 5 · 2026-04-12 10:13:55

36

Views

Decay of Fourier coefficients of a smooth family of functions

Published on 12 Apr 2026 - 10:13

score 25 · Answer 6 · 2026-04-09 07:46:52

25

Views

Confusing about calculating a value with Fourier complex inversion formula

Published on 09 Apr 2026 - 7:46

score 57 · Answer 7 · 2026-04-14 10:06:36

57

Views

Fourier transform and inverse calculations without residues and cauchy theorem

Published on 14 Apr 2026 - 10:06

score 195 · Answer 8 · 2026-04-13 01:18:44

195

Views

Cartesian parametrization of the Greek Meandre

Published on 13 Apr 2026 - 1:18

score 194 · Answer 9 · 2026-04-15 18:26:41

194

Views

Probability measures on the hypersphere $\Bbb S^{n-1}$ and the $O(n)$ isomorphisms

Published on 15 Apr 2026 - 18:26

score 45 · Answer 10 · 2026-04-10 04:44:20

45

Views

Fourier analysis problem

Published on 10 Apr 2026 - 4:44

score 34 · Answer 11 · 2026-04-15 03:58:11

34

Views

Show that $\sum_{n=1}^{\infty}(-1)^n\frac{\sin(nx)}{n} = \frac{-x}{2}$ for $-\pi < x < \pi$.

Published on 15 Apr 2026 - 3:58

score 38 · Answer 12 · 2026-04-15 07:50:11

38

Views

Convergent sequences defining the topology on a space.

Published on 15 Apr 2026 - 7:50

score 22 · Answer 13 · 2026-04-13 00:54:11

22

Views

Decay in Fourier coefficients

Published on 13 Apr 2026 - 0:54

score 59 · Answer 14 · 2026-04-17 07:18:34

59

Views

If Fourier transform of a simple function $f$ satisfies inequality $\| \hat{f} \|_q \leq C\|f\|_p$ then $1/p + 1/q = 1$

Published on 17 Apr 2026 - 7:18

score 79 · Answer 15 · 2026-04-12 17:48:34

79

Views

Using the Banach-Steinhaus Theorem to show the existence of a divergent Fourier series

Published on 12 Apr 2026 - 17:48

List Question

If $f \in L^p(\Bbb R)$ for $1 < p\le 2$, then $f\ast \frac{\sin \pi t}{\pi t} \in L^p(\Bbb R)$.

Find $\min \sum |a_n|$ when $\sum |a_n|^2 = 1$ and $\sum |a_n|^4 = \lambda$ (Katznelson's Ex $4.1.2.$)

Identify Closed Subgroup in Compact Abelian Group

Error with Fourier Transform

Decay of Fourier coefficients of a smooth family of functions

Confusing about calculating a value with Fourier complex inversion formula

Fourier transform and inverse calculations without residues and cauchy theorem

Cartesian parametrization of the Greek Meandre

Probability measures on the hypersphere $\Bbb S^{n-1}$ and the $O(n)$ isomorphisms

Fourier analysis problem

Show that $\sum_{n=1}^{\infty}(-1)^n\frac{\sin(nx)}{n} = \frac{-x}{2}$ for $-\pi < x < \pi$.

Convergent sequences defining the topology on a space.

Decay in Fourier coefficients

If Fourier transform of a simple function $f$ satisfies inequality $\| \hat{f} \|_q \leq C\|f\|_p$ then $1/p + 1/q = 1$

Using the Banach-Steinhaus Theorem to show the existence of a divergent Fourier series

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