List questions from fourier-analysis

Published on 16 Apr 2026 - 2:47

128

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Proof of Corollary 2.4 in Stein and Shakarachi Fourier Analysis

Published on 12 Apr 2026 - 5:19

43

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Even Function Fourier Expansion

Published on 09 Apr 2026 - 1:10

560

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Verification of Orthogonality Integral by Direct Integration

Published on 11 Apr 2026 - 12:22

177

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Can Fourier techniques still be useful in situations where we don't have perfect periodicity (such as a missing point in a lattice)?

Published on 24 Apr 2026 - 2:57

46

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How to define $H^k(\Omega)$ given this definition of $H^k(T^n)?$

Published on 10 Apr 2026 - 9:41

22

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How to show that the following function is Schwarz

Published on 17 Apr 2026 - 12:45

702

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The Continuous Differential Operator

Published on 10 Apr 2026 - 8:06

88

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Fourier coefficients of sine waveform

Published on 09 Apr 2026 - 7:06

268

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If $|\hat{f}(k)| \leq e^{-|k|},$ then what can we say about $f$?

Published on 14 Apr 2026 - 19:17

94

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Given a fourier transform of a function, what does it give me in regards to the Fourier series?

Published on 11 Apr 2026 - 1:38

28

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fourier coeffitient of $[f]_{\dot{C}^{\alpha}}:=sup_{x,y\in[0,2\pi]}\frac{|f(x)-f(y)|}{|x-y|^{\alpha}}<\infty, \ \ \ \ \alpha\in(0,1].$

Published on 13 Apr 2026 - 19:25

44

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Deriving integral formula for Fourier transform of $L^1$ functions

Published on 14 Apr 2026 - 10:22

252

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Fourier multiplier and applications

Published on 09 Apr 2026 - 15:29

371

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For $C>0$, computing Fourier transform of indicator function $\chi_{[0,C]}$

Published on 16 Apr 2026 - 9:13

List Question

Is $L^1(\mathbb{R}^n)\cap L^2(\mathbb{R}^n)$ dense in $L^2(\mathbb{R}^n)$?

Proof of Corollary 2.4 in Stein and Shakarachi Fourier Analysis

Even Function Fourier Expansion

Verification of Orthogonality Integral by Direct Integration

Can Fourier techniques still be useful in situations where we don't have perfect periodicity (such as a missing point in a lattice)?

How to define $H^k(\Omega)$ given this definition of $H^k(T^n)?$

How to show that the following function is Schwarz

The Continuous Differential Operator

Fourier coefficients of sine waveform

If $|\hat{f}(k)| \leq e^{-|k|},$ then what can we say about $f$?

Given a fourier transform of a function, what does it give me in regards to the Fourier series?

fourier coeffitient of $[f]_{\dot{C}^{\alpha}}:=sup_{x,y\in[0,2\pi]}\frac{|f(x)-f(y)|}{|x-y|^{\alpha}}<\infty, \ \ \ \ \alpha\in(0,1].$

Deriving integral formula for Fourier transform of $L^1$ functions

Fourier multiplier and applications

For $C>0$, computing Fourier transform of indicator function $\chi_{[0,C]}$

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