Question

Eigenvectors of Dual of Left Shift Operator

score 473 · Answer 1 · 2026-04-08 02:37:00

473

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Eigenvectors of Dual of Left Shift Operator

Published on 08 Apr 2026 - 2:37

score 108 · Answer 2 · 2017-10-03 12:14:18

108

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Does their exist a real continuous function other than $f(x)=0$ such that $f(2x) = -2f(x)$?

Published on 03 Oct 2017 - 12:14

score 66 · Answer 3 · 2026-04-07 23:55:45

66

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Continuous function and function relationship

Published on 07 Apr 2026 - 23:55

score 323 · Answer 4 · 2017-10-04 02:54:09

323

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If $f(1)=1$, then is it true that $f(n)=n$ for all $n \in \mathbb{N}\cup\{0\}$.

Published on 04 Oct 2017 - 2:54

score 143 · Answer 5 · 2017-10-04 15:43:15

143

Views

What can be $f$ so that $f(f(x)) = -x$?

Published on 04 Oct 2017 - 15:43

score 186 · Answer 6 · 2026-03-26 00:53:58

186

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find strictly increasing function $f:\mathbb{N}\rightarrow \mathbb{R}$ such that $f(2)=2$ and $f(x\cdot y)=f(x)\cdot f(y)$ when $\gcd(x,y)=1$

Published on 26 Mar 2026 - 0:53

score 21 · Answer 7 · 2017-10-06 08:08:30

21

Views

Numerical frameworks for solving completely arbitrary functio-differential equations?

Published on 06 Oct 2017 - 8:08

score 281 · Answer 8 · 2026-04-08 04:42:43

281

Views

Oxford MAT functional equation question

Published on 08 Apr 2026 - 4:42

score 147 · Answer 9 · 2026-03-25 11:08:53

147

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How do you solve this functional equation?

Published on 25 Mar 2026 - 11:08

score 80 · Answer 10 · 2017-10-11 18:32:38

80

Views

Proof by contradiction$\,-\,$functional equation

Published on 11 Oct 2017 - 18:32

score 124 · Answer 11 · 2017-10-13 07:41:32

124

Views

Find all functions $f(m)[(f(n))^2-1]=f(n)[f(m+n)-f(m-n)]$

Published on 13 Oct 2017 - 7:41

score 195 · Answer 12 · 2017-10-13 18:08:25

195

Views

Find all $f : \mathbb{N} \to \mathbb{N}$ such that $f(a) + f(b) \mid a+b, \ \forall \ a, b \in \mathbb{N}$

Published on 13 Oct 2017 - 18:08

score 824 · Answer 13 · 2017-10-15 12:23:33

824

Views

$f:\mathbb{R}\rightarrow\mathbb{R}$ is not one-to-one if $[f(x)]^2-4\cdot f(x^5)+3=0,\forall x\in\mathbb{R}$?

Published on 15 Oct 2017 - 12:23

score 114 · Answer 14 · 2017-10-15 21:41:53

114

Views

Find all $f:\mathbb{R}\to\mathbb{R}$ with $f(x+f(y))=f(x)-f(y)$

Published on 15 Oct 2017 - 21:41

score 135 · Answer 15 · 2017-10-17 14:19:00

135

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How to solve differential-functional equation?

Published on 17 Oct 2017 - 14:19

List Question

Eigenvectors of Dual of Left Shift Operator

Does their exist a real continuous function other than $f(x)=0$ such that $f(2x) = -2f(x)$?

Continuous function and function relationship

If $f(1)=1$, then is it true that $f(n)=n$ for all $n \in \mathbb{N}\cup\{0\}$.

What can be $f$ so that $f(f(x)) = -x$?

find strictly increasing function $f:\mathbb{N}\rightarrow \mathbb{R}$ such that $f(2)=2$ and $f(x\cdot y)=f(x)\cdot f(y)$ when $\gcd(x,y)=1$

Numerical frameworks for solving completely arbitrary functio-differential equations?

Oxford MAT functional equation question

How do you solve this functional equation?

Proof by contradiction$\,-\,$functional equation

Find all functions $f(m)[(f(n))^2-1]=f(n)[f(m+n)-f(m-n)]$

Find all $f : \mathbb{N} \to \mathbb{N}$ such that $f(a) + f(b) \mid a+b, \ \forall \ a, b \in \mathbb{N}$

$f:\mathbb{R}\rightarrow\mathbb{R}$ is not one-to-one if $[f(x)]^2-4\cdot f(x^5)+3=0,\forall x\in\mathbb{R}$?

Find all $f:\mathbb{R}\to\mathbb{R}$ with $f(x+f(y))=f(x)-f(y)$

How to solve differential-functional equation?

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