Question

Showing that the sequence $\Big(\frac{e^{int}}{\sqrt{2\pi}}\Big)_{n=1}^{\infty}$ is an orthonormal basis for $L^2 ((-\pi, \pi))$

score 1.4k · Answer 1 · 2026-03-25 08:12:50

1.4k

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Showing that the sequence $\Big(\frac{e^{int}}{\sqrt{2\pi}}\Big)_{n=1}^{\infty}$ is an orthonormal basis for $L^2 ((-\pi, \pi))$

Published on 25 Mar 2026 - 8:12

score 73 · Answer 2 · 2018-04-04 17:20:48

73

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The metric on L2 space expressed in terms of Fourier sine coefficients

Published on 04 Apr 2018 - 17:20

score 49 · Answer 3 · 2026-03-20 11:40:06

49

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When does $0=\int f(x)\psi(x)\,dx$ for all $f\in L^1(G)$ imply that $\psi=0$

Published on 20 Mar 2026 - 11:40

score 388 · Answer 4 · 2018-04-08 11:22:17

388

Views

Convergence in Skorokhod topology implies convergence in $L^1$.

Published on 08 Apr 2018 - 11:22

score 281 · Answer 5 · 2018-04-09 02:11:53

281

Views

Mean square derivative of square of WSS (wide sense stationary) Gaussian RP

Published on 09 Apr 2018 - 2:11

score 184 · Answer 6 · 2018-04-09 05:02:25

184

Views

Proof of : Norm of Linear transformation from Rn (equipped with sup-norm) to Rm (equipped with l1 norm)

Published on 09 Apr 2018 - 5:02

score 141 · Answer 7 · 2018-04-09 23:01:04

141

Views

Proving that pointwise limit implies limit of a sequence in $\ell^p$

Published on 09 Apr 2018 - 23:01

score 84 · Answer 8 · 2018-04-11 15:52:20

84

Views

Show that sequence converges, hence find the limit.

Published on 11 Apr 2018 - 15:52

score 264 · Answer 9 · 2018-04-11 20:01:24

264

Views

Basis for $L^2(0,1)$ and $H^2(0,1)\times L^2(0,1)$ defined on complex field

Published on 11 Apr 2018 - 20:01

score 444 · Answer 10 · 2018-04-12 02:51:33

444

Views

The $L_p$-norm of sum of a function and its translation at infinity

Published on 12 Apr 2018 - 2:51

score 542 · Answer 11 · 2018-04-12 09:15:51

542

Views

inverse Minkowski inequality for $p \in (0,1)$

Published on 12 Apr 2018 - 9:15

score 137 · Answer 12 · 2018-04-12 19:25:55

137

Views

Strong convergence of a product of weakly converging functions

Published on 12 Apr 2018 - 19:25

score 43 · Answer 13 · 2018-04-13 01:49:50

43

Views

Showing that the $L^2$ inequality does not hold

Published on 13 Apr 2018 - 1:49

score 67 · Answer 14 · 2018-04-13 01:52:20

67

Views

Prove a set is nowhere dense

Published on 13 Apr 2018 - 1:52

score 346 · Answer 15 · 2018-04-13 14:15:30

346

Views

When a multiplication operator $M_\phi$ satisfies in ${M_\phi}^{2}=M_\phi$?

Published on 13 Apr 2018 - 14:15

List Question

Showing that the sequence $\Big(\frac{e^{int}}{\sqrt{2\pi}}\Big)_{n=1}^{\infty}$ is an orthonormal basis for $L^2 ((-\pi, \pi))$

The metric on L2 space expressed in terms of Fourier sine coefficients

When does $0=\int f(x)\psi(x)\,dx$ for all $f\in L^1(G)$ imply that $\psi=0$

Convergence in Skorokhod topology implies convergence in $L^1$.

Mean square derivative of square of WSS (wide sense stationary) Gaussian RP

Proof of : Norm of Linear transformation from Rn (equipped with sup-norm) to Rm (equipped with l1 norm)

Proving that pointwise limit implies limit of a sequence in $\ell^p$

Show that sequence converges, hence find the limit.

Basis for $L^2(0,1)$ and $H^2(0,1)\times L^2(0,1)$ defined on complex field

The $L_p$-norm of sum of a function and its translation at infinity

inverse Minkowski inequality for $p \in (0,1)$

Strong convergence of a product of weakly converging functions

Showing that the $L^2$ inequality does not hold

Prove a set is nowhere dense

When a multiplication operator $M_\phi$ satisfies in ${M_\phi}^{2}=M_\phi$?

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