# Questions tagged [periodic-functions]

Questions on periodic functions, functions $f(x)$ that satisfy the identity $f(x+c)=f(x)$, for some nonzero $c$.

944 questions
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### Principal value definition of the fractional Laplacian on the torus

I have a periodic function $u$ defined on the torus $\mathbb{T}^2= \mathbb{R}^2/\mathbb{Z^2}$ and want to find the corresponding definition of the fractional Laplacian $(-\Delta^{s})u$ in terms of the ...
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### Fundamental frequency of the sum of two sinusoids

I'm trying to find the fundamental frequency of $\cos(23t + \pi/2) + \sin(5t + \pi/5)$ Now the period for both are $2\pi/23$ and $2\pi/5$ respectively. So i need to find the LCM of these two ...
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### Why is the fundamental period of $\sin^3(2t)$ given by $1/\pi$ rather than $\pi$?

Take a look at the following function: $$x(t) = \sin^3(2t)$$ In order to show the periodicity of the signal, we need to prove the following equality $$x(t) = x(t+T)$$ We first use some ...
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### Literature request - finite Fourier series expansion of bounded, periodic, differentiable functions?

Question - Is someone aware of a published work proving the following: Every bounded, differentiable, periodic function of $n$ variables has a Fourier Series expansion with exactly $m$ terms ($m$ is ...
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### Can the sum of two periodic functions over $\mathbb R$ be strictly increasing?

If there exists a direct sum decomposition for the real space $\mathbb R=V\oplus W$, and define $f(v+w)=v$, $g(v+w)=w$, then $h(v+w)=v+w$ is strictly increasing. But I can't find explicitly one such ...
My equation of interest is a logistic growth model affected by a sinusoidal oscillation. $$\frac{dN}{dt}=(rN(c-N)-\mu N)(1+cos(2\pi t))$$ I want to show a periodic solution exists so I was thinking ...