List questions from even-and-odd-functions

Published on 30 Nov 2021 - 19:08

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Why is $\hat f(\xi)/\xi\in L^1(\mathbb R)$ when $f\in L^1$ is odd,$\hat f'(0)$ exists, and $\hat f(\xi)$ always has the same sign as $\xi$?

Published on 10 Dec 2021 - 8:24

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Even Extension of Heat Equation on Semi-Infinte Domain

Published on 11 Dec 2021 - 0:18

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$f(a)+f(-b)=0$ implies $f(-a)+f(b)=0$. Then $f$ is an odd function?

Published on 07 Jan 2022 - 10:06

48

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For any $(a,b)\in\mathbb R^2$ such that $2f(a)+f(-b)\geq 0$, we have: $2f(-a)+f(b)\leq 0$. Then, $f$ must be an odd function?

Published on 07 Jan 2022 - 10:41

50

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Is this function odd with respect to $x$?

Published on 11 Jan 2022 - 18:05

60

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Would this be an even or odd function?

Published on 17 Jan 2022 - 17:05

90

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Sum of roots for a even function and slope being 0?

Published on 21 Jan 2022 - 3:49

64

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Solving summation of fractional powers with floor

Published on 30 Jan 2022 - 23:21

60

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Can I see from here if this integral is zero?

Published on 03 Feb 2022 - 13:58

51

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Constructing holomorphic odd functions

Published on 10 Feb 2022 - 16:18

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What is the decomposition into even and odd function of a function equal to $x$ when $x \geq 0$ and equal to zero when $x <0$?

Published on 13 Feb 2022 - 21:36

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solving definite integral with properties

Published on 01 Mar 2022 - 22:16

68

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It makes sense to consider oddness with respect a point which is not $0$?

Published on 07 Mar 2022 - 15:30

76

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Construct a function $f$ with $f'-af$ is odd (a>0)

Published on 17 Mar 2022 - 15:23

List Question

Is $f(\theta) = 1 - \alpha \sin{\theta}$ an odd function?

Why is $\hat f(\xi)/\xi\in L^1(\mathbb R)$ when $f\in L^1$ is odd,$\hat f'(0)$ exists, and $\hat f(\xi)$ always has the same sign as $\xi$?

Even Extension of Heat Equation on Semi-Infinte Domain

$f(a)+f(-b)=0$ implies $f(-a)+f(b)=0$. Then $f$ is an odd function?

For any $(a,b)\in\mathbb R^2$ such that $2f(a)+f(-b)\geq 0$, we have: $2f(-a)+f(b)\leq 0$. Then, $f$ must be an odd function?

Is this function odd with respect to $x$?

Would this be an even or odd function?

Sum of roots for a even function and slope being 0?

Solving summation of fractional powers with floor

Can I see from here if this integral is zero?

Constructing holomorphic odd functions

What is the decomposition into even and odd function of a function equal to $x$ when $x \geq 0$ and equal to zero when $x <0$?

solving definite integral with properties

It makes sense to consider oddness with respect a point which is not $0$?

Construct a function $f$ with $f'-af$ is odd (a>0)

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