List questions from fourier-analysis

22

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If $f \in L^2(\mathbb{R}^n)$ and $T \in S^*(\mathbb{R}^n)$. Then: there exists $F \in L^2(\mathbb{R}^n)$ such that $\hat{T}_f=T_F$

Published on 16 Apr 2026 - 21:36

244

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Intuition for how the Fourier transform "preserves information" and "changes basis"?

Published on 14 Apr 2026 - 19:31

72

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Explicit example of a Fourier transform of $f \in L^2(\mathbb R) \setminus L^1(\mathbb R)$

Published on 14 Apr 2026 - 10:46

53

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Integral of product of Bessel functions of different order

Published on 14 Apr 2026 - 14:34

36

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Complex Form of the Fourier transform

Published on 14 Apr 2026 - 7:07

311

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Fourier Uncertainty Principle

Published on 09 Apr 2026 - 1:18

48

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Fourier Series of a non periodic function

Published on 11 Apr 2026 - 13:01

53

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Introduction to Fourier Analysis Question, Chapter 6 exercise 7

Published on 13 Apr 2026 - 13:20

53

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Product of a Schwartz function and a tempered distribution

Published on 14 Apr 2026 - 11:52

49

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Trying to understand the functional calculus of a unitary operator.

Published on 09 Apr 2026 - 7:31

61

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Asymptotic expression for Fourier Transform of $e^{-|x|^n}$?

Published on 24 Apr 2026 - 18:33

69

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Obtain $L^\infty$ estimate of Poisson Equation only using eigenfunction expansion

Published on 10 Apr 2026 - 16:48

139

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Approximating the Box Function as a sum of sinusoids using the Inverse Fourier Transform

Published on 12 Apr 2026 - 19:14

114

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Why is the solution of the Klein-Gordon PDE a distribution?

Published on 13 Apr 2026 - 1:38

58

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Fourier transform theorem proof help

Published on 08 Apr 2026 - 22:37

List Question

If $f \in L^2(\mathbb{R}^n)$ and $T \in S^*(\mathbb{R}^n)$. Then: there exists $F \in L^2(\mathbb{R}^n)$ such that $\hat{T}_f=T_F$

Intuition for how the Fourier transform "preserves information" and "changes basis"?

Explicit example of a Fourier transform of $f \in L^2(\mathbb R) \setminus L^1(\mathbb R)$

Integral of product of Bessel functions of different order

Complex Form of the Fourier transform

Fourier Uncertainty Principle

Fourier Series of a non periodic function

Introduction to Fourier Analysis Question, Chapter 6 exercise 7

Product of a Schwartz function and a tempered distribution

Trying to understand the functional calculus of a unitary operator.

Asymptotic expression for Fourier Transform of $e^{-|x|^n}$?

Obtain $L^\infty$ estimate of Poisson Equation only using eigenfunction expansion

Approximating the Box Function as a sum of sinusoids using the Inverse Fourier Transform

Why is the solution of the Klein-Gordon PDE a distribution?

Fourier transform theorem proof help

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