Question

Does $ \frac{1}{N} \sum_{n=-N^2}^{N^2} f(\tfrac{n}{N}) \to \int_{-\infty}^\infty f(x) \, dx $ work for integrable functions?

score 92 · Answer 1 · 2026-03-28 15:21:26

92

Views

Does $ \frac{1}{N} \sum_{n=-N^2}^{N^2} f(\tfrac{n}{N}) \to \int_{-\infty}^\infty f(x) \, dx $ work for integrable functions?

Published on 28 Mar 2026 - 15:21

score 57 · Answer 2 · 2026-02-23 01:23:34

57

Views

If the integral of a function is known, can anything be said about products of integrals of the function and its Fourier transform?

Published on 23 Feb 2026 - 1:23

score 306 · Answer 3 · 2026-03-26 12:53:00

306

Views

Fourier Expansion in Siegel Modular forms

Published on 26 Mar 2026 - 12:53

score 188 · Answer 4 · 2026-03-30 15:14:46

188

Views

Growth of the Fourier transform of a compact function

Published on 30 Mar 2026 - 15:14

score 202 · Answer 5 · 2026-03-30 15:13:06

202

Views

Confused of the Poisson kernel for upper half-plane

Published on 30 Mar 2026 - 15:13

score 39 · Answer 6 · 2019-09-03 09:09:08

39

Views

Families of functions with "frequency is polynomial" property.

Published on 03 Sep 2019 - 9:09

score 943 · Answer 7 · 2026-03-28 03:29:53

943

Views

Characteristic functions agree in a neighborhood of zero

Published on 28 Mar 2026 - 3:29

score 1.6k · Answer 8 · 2026-03-30 03:55:13

1.6k

Views

Why the Fourier series for this discontinuous function doesn't give the correct behavior near the discontinuity?

Published on 30 Mar 2026 - 3:55

score 29 · Answer 9 · 2026-03-29 12:33:21

29

Views

Connection between the Laplace transform of two functions

Published on 29 Mar 2026 - 12:33

score 99 · Answer 10 · 2026-03-25 01:20:19

99

Views

How do summations/integrals like Fourier, Laplace, z-transforms preserve all the information about the original signal?

Published on 25 Mar 2026 - 1:20

score 124 · Answer 11 · 2026-03-26 06:07:03

124

Views

4D Fourier transforms of $\exp(-\frac{||\vec{x}||_2}{2})$

Published on 26 Mar 2026 - 6:07

score 257 · Answer 12 · 2019-09-07 13:02:36

257

Views

A Proof of Series of A Product of Fourier Coefficients Converges Absolutely

Published on 07 Sep 2019 - 13:02

score 2.3k · Answer 13 · 2026-04-05 07:48:13

2.3k

Views

Subscript Notation on Real Numbers

Published on 05 Apr 2026 - 7:48

score 57 · Answer 14 · 2026-03-30 20:56:02

57

Views

Prove that if $g(x) = f(\alpha x)$, then $\hat{g}(w) = \frac{\hat{f}(\frac{w}{\alpha})}{|\alpha|}$.

Published on 30 Mar 2026 - 20:56

score 85 · Answer 15 · 2026-03-26 06:42:45

85

Views

If a trigonometric series converges to a function $f$, is the Fourier series of $f$ the original series?

Published on 26 Mar 2026 - 6:42

List Question

Does $ \frac{1}{N} \sum_{n=-N^2}^{N^2} f(\tfrac{n}{N}) \to \int_{-\infty}^\infty f(x) \, dx $ work for integrable functions?

If the integral of a function is known, can anything be said about products of integrals of the function and its Fourier transform?

Fourier Expansion in Siegel Modular forms

Growth of the Fourier transform of a compact function

Confused of the Poisson kernel for upper half-plane

Families of functions with "frequency is polynomial" property.

Characteristic functions agree in a neighborhood of zero

Why the Fourier series for this discontinuous function doesn't give the correct behavior near the discontinuity?

Connection between the Laplace transform of two functions

How do summations/integrals like Fourier, Laplace, z-transforms preserve all the information about the original signal?

4D Fourier transforms of $\exp(-\frac{||\vec{x}||_2}{2})$

A Proof of Series of A Product of Fourier Coefficients Converges Absolutely

Subscript Notation on Real Numbers

Prove that if $g(x) = f(\alpha x)$, then $\hat{g}(w) = \frac{\hat{f}(\frac{w}{\alpha})}{|\alpha|}$.

If a trigonometric series converges to a function $f$, is the Fourier series of $f$ the original series?

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