# Tagged Questions

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### Convolution: $f (-)*g = g(-)* f$ does this mean both $f$ and $g$ have to be even functions?

Assuming $f$ and $g$ are different functions, does $f (-)*g = g(-)* f$ mean both $f$ and $g$ have to be even functions? In fact, this is equivalent to $f\star g = g \star f$ (i.e., cross-correlation ...
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### Intuition behind the convolution of two functions

Suppose $f(x)$ and $g(x)$ are two functions. What is intuition or idea behind the convolution of $f$ and $g$? After taking the convolution we will get a new function. What is the geometric relation ...
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### Show $\exists f \in C \ni \|f\|_\infty \le 1$, but it's Fourier series diverges

Show $\exists f \in C \ni \|f\|_\infty \le 1$, but it's Fourier series diverges. The proof is in our textbook (Katznelson, Harmonic analysis). It uses this argument. Let ...
### Cesaro summable implies that $c_{n}/n$ goes to $0$
Theorem. If $\sum_{n=1}^{\infty}c_{n}$ is Cesaro summable, then $c_{n}/n$ tends to $0$. How to prove it?