Computing a FourierTransform
We have $M:= \left \{ \left(\begin{array}{c} x \\ y \end{array} \right ) \in \mathbb{R}^2 ; \left  \left  \left(\begin{array}{c} x \\ y \end{array} \right )  \left(\begin{array}{c} 0 \\ \frac{1}{\sqrt{2} } \end{array} \right ) \right  \right _1 \leq \frac{1}{\sqrt{2} } \right \}$.
Compute the FourierTransform of the charactersitic function of $M$, i.e.
$\chi_M : \mathbb{R}^2 \rightarrow \mathbb{R}, \quad v \mapsto \begin{cases} 1 & v \in M \\ 0 & v \notin M \end{cases}$.
Do that by using the following hint:
$\textbf{Hint}$: Consider the matrix $A= \frac{1}{\sqrt{2} } \begin{pmatrix} 1 & 1 \\ 1 & 1\end{pmatrix}$ first and determine the set $AM = \{ A \cdot v ; v \in M \}$.
Answer
 The questioner was satisfied and accepted the answer, or
 The answer was disputed, but the judge evaluated it as 100% correct.

are you able to put it in latex? if not, I can copy the question and afterwards accept the answer here

I've tried to rewrite my solution that was deleted rather hastily  if there's any problem or typo let me know. Sorry for the inconvenience.
 answered
 211 views
 $8.76
Related Questions
 Parsevals theorem problem
 Find amplitudefrequency characteristic of a discrete finite signal using Ztransform
 Integration with plancherels theorem
 Plot real and imaginary part, modulus, phase and imaginary plane for a CFT transform given by equation on f from 4Hz to 4Hz
 Antiderivative of a Schwartzfunction