Question

Find the complex Fourier series of the $2\pi$ periodic function $f(x)=x^2$ and determine the function which the Fourier series converges to.

score 793 · Answer 1 · 2026-05-14 05:18:48

793

Views

Find the complex Fourier series of the $2\pi$ periodic function $f(x)=x^2$ and determine the function which the Fourier series converges to.

Published on 14 May 2026 - 5:18

score 122 · Answer 2 · 2026-05-10 20:17:24

122

Views

Region of convergence of the Laplace transform

Published on 10 May 2026 - 20:17

score 733 · Answer 3 · 2026-04-13 06:40:37

733

Views

Fourier series for $f(x+\pi) = f(x)$

Published on 13 Apr 2026 - 6:40

score 315 · Answer 4 · 2026-05-10 15:47:51

315

Views

Limit of sequence of finite rank operators given by $(A_Nf)(x) = \sum_{n=-N}^N \hat f(n) e^{inx}$ is the identity operator, so how can it be compact?

Published on 10 May 2026 - 15:47

score 40 · Answer 5 · 2026-05-11 04:42:07

40

Views

Prove that $\lim_{N \to \infty} \left( \int_{\pi-\pi/(N+1/2)}^{\pi} \frac{\sin((N+1/2)t)}{\sin(t/2)} dt \right)= 0$

Published on 11 May 2026 - 4:42

score 50 · Answer 6 · 2026-04-15 21:53:30

$\{f \in L^1(\mathbb R^n) \cap L^2(\mathbb R^n): \mathcal Ff \in L^2(\mathbb R^n)\}$ dense in $L^1(\mathbb R^n) \cap L^2(\mathbb R^n)$?

score 77 · Answer 7 · 2026-05-10 19:48:50

77

Views

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

Published on 10 May 2026 - 19:48

score 494 · Answer 8 · 2026-05-11 04:37:18

494

Views

Find Fourier Series of $f(x)=e^x+e^{-x}$

Published on 11 May 2026 - 4:37

score 147 · Answer 9 · 2026-05-05 06:27:44

147

Views

An elementary (interpolation) inequality?

Published on 05 May 2026 - 6:27

score 667 · Answer 10 · 2026-05-14 13:07:15

667

Views

On the asymptotic behavior of the Fourier coefficients of $(1-R\cos\theta)^{-3/2}$

Published on 14 May 2026 - 13:07

score 1.7k · Answer 11 · 2026-05-11 04:42:07

1.7k

Views

How to prove that the span of $\cos((n+1/2)x)$ and $\sin(nx)$ is dense in $L^2(-\pi,\pi)$?

Published on 11 May 2026 - 4:42

score 45 · Answer 12 · 2026-05-14 06:24:15

45

Views

Sovling classical parabolic equation by using Littlewood-Paley theory

Published on 14 May 2026 - 6:24

score 55 · Answer 13 · 2026-04-12 23:31:20

55

Views

Evaluating integrals of periodic functions

Published on 12 Apr 2026 - 23:31

score 158 · Answer 14 · 2026-05-10 13:10:58

158

Views

What is the Fourier transform of a "geometric delta comb?"

Published on 10 May 2026 - 13:10

score 99 · Answer 15 · 2026-04-11 05:34:21

99

Views

Stationary phase analysis for a Schwartz function

Published on 11 Apr 2026 - 5:34

List Question

Find the complex Fourier series of the $2\pi$ periodic function $f(x)=x^2$ and determine the function which the Fourier series converges to.

Region of convergence of the Laplace transform

Fourier series for $f(x+\pi) = f(x)$

Limit of sequence of finite rank operators given by $(A_Nf)(x) = \sum_{n=-N}^N \hat f(n) e^{inx}$ is the identity operator, so how can it be compact?

Prove that $\lim_{N \to \infty} \left( \int_{\pi-\pi/(N+1/2)}^{\pi} \frac{\sin((N+1/2)t)}{\sin(t/2)} dt \right)= 0$

$\{f \in L^1(\mathbb R^n) \cap L^2(\mathbb R^n): \mathcal Ff \in L^2(\mathbb R^n)\}$ dense in $L^1(\mathbb R^n) \cap L^2(\mathbb R^n)$?

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

Find Fourier Series of $f(x)=e^x+e^{-x}$

An elementary (interpolation) inequality?

On the asymptotic behavior of the Fourier coefficients of $(1-R\cos\theta)^{-3/2}$

How to prove that the span of $\cos((n+1/2)x)$ and $\sin(nx)$ is dense in $L^2(-\pi,\pi)$?

Sovling classical parabolic equation by using Littlewood-Paley theory

Evaluating integrals of periodic functions

What is the Fourier transform of a "geometric delta comb?"

Stationary phase analysis for a Schwartz function

Trending Questions

Popular # Hahtags

Popular Questions