Heisenberg inequality on the real line

A quantum mechanical principle discovered by Werner Heisenberg states that it is not possible to simultaneously determine the position and momentum of a particle. In fact, this principle is deeply mathematical and independent from the experimental precision of the instruments. We illustrate how it can be expressed for functions on the real line.

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Fourier Transform over Finite Abelian Groups

Here is an overview of Fourier analysis applied to finite abelian groups. It shows how to generalize a priori different computations such as the discrete Fourier transform or the Hadamard-Walsh transform.


Let G be a finite abelian group with additive notation. A character of G is a group homomorphism \chi : G \rightarrow \mathbb{C} - \{ 0 \} that is to say for all a , b \in G

\displaystyle \chi ( a + b ) = \chi ( a ) \chi ( b )

\displaystyle \chi ( 0 ) = 1

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