# Questions tagged [periodic-functions]

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

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### Floquet theorem for Hilbert spaces

Can the Floquet theorem be generalized to Hilbert spaces? I think the generalization would look something like this: Consider a dynamical system $\dot{x}(t)=A(t)x(t)$, where $A(t)$ is a family of ...
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### Number of subsequences of consecutive sequences in a non-periodic sequence

Let $a_1, a_2, \ldots$ be a sequence which is not eventually periodic, i.e. there do not exist constants $K$ and $N$ such that $a_m = a_{m+K}$ for all $m \geq N$. Prove that the number of distinct ...
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I'm trying to prove something about periodic functions and I'd need someone to tell me if what I wrote is right! If $f$ is a periodic function with fundamental period $\tau$. Then, all periods of $f$ ...
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### Fourier transform of periodic distributions & local application of a result

Context: I am currently working through Chapter $8$ of Anders Vretblad's Fourier Analysis and Its Applications. This particular chapter focuses on distributions, and builds up to the Fourier transform ...
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Given $q$ a prime number , $a$ a primitive root modulo $q$ and $b=a^x \pmod q$. The discrete logarithm problem is to find $x$ (specifically the smallest positive integer $x$ for which the previous ...