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 · 2026-05-10 16:14:33

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 10 May 2026 - 16:14

score 76 · Answer 2 · 2026-04-12 09:38:32

76

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

Published on 12 Apr 2026 - 9:38

score 56 · Answer 3 · 2026-05-05 08:19:35

56

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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 05 May 2026 - 8:19

score 391 · Answer 4 · 2026-04-14 14:58:32

391

Views

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

Published on 14 Apr 2026 - 14:58

score 285 · Answer 5 · 2026-05-10 14:49:19

285

Views

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

Published on 10 May 2026 - 14:49

score 187 · Answer 6 · 2026-04-08 20:58:24

187

Views

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

Published on 08 Apr 2026 - 20:58

score 144 · Answer 7 · 2026-04-16 09:16:48

144

Views

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

Published on 16 Apr 2026 - 9:16

score 86 · Answer 8 · 2026-04-14 00:58:41

86

Views

Show that sequence converges, hence find the limit.

Published on 14 Apr 2026 - 0:58

score 268 · Answer 9 · 2026-05-10 17:15:04

268

Views

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

Published on 10 May 2026 - 17:15

score 447 · Answer 10 · 2026-04-13 10:22:49

447

Views

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

Published on 13 Apr 2026 - 10:22

score 545 · Answer 11 · 2026-04-15 11:32:27

545

Views

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

Published on 15 Apr 2026 - 11:32

score 141 · Answer 12 · 2026-05-10 17:15:42

141

Views

Strong convergence of a product of weakly converging functions

Published on 10 May 2026 - 17:15

score 46 · Answer 13 · 2026-04-11 07:31:38

46

Views

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

Published on 11 Apr 2026 - 7:31

score 70 · Answer 14 · 2026-04-15 07:41:53

70

Views

Prove a set is nowhere dense

Published on 15 Apr 2026 - 7:41

score 349 · Answer 15 · 2026-04-16 03:55:39

349

Views

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

Published on 16 Apr 2026 - 3:55

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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