Impulse response of a time scaling system Assume a bandlimited signal $X(t)$. Given that the output for this signal is $X(t/2)$, what will be the impulse response $h(t)$ of such a system?

\begin{array}{l}
X( \omega ) \ =\ \int ^{\infty }_{-\infty } x( t) e ^{-j\omega t} dt  \\
Y( \omega ) \ =2X( 2\omega )\\
\end{array}

As the system won't be LTI the output won't be the convolution of the input and the system response. How do I proceed with finding the response of such a system? Any guidance in the direction of the solution will be very helpful. 

Edit: Thanks for all the answers, i had reframed this question which was on a similar line. The question goes like this -> 
Given an input pulse of duration T, the system scales it to a pulse of 2T, design such a system? It would be of great help if someone could point out the right direction to proceed.
The input-output relation of such a system can be written as

$$y(t)=\int_{-\infty}^{\infty}\delta(t/2-\tau)x(\tau)d\tau\tag{1}$$

Note that the system is linear but time-varying, and such systems can generally be described by a two-dimensional impulse response $h(t,\tau)$:

$$y(t)=\int_{-\infty}^{\infty}h(t,\tau)x(\tau)d\tau\tag{2}$$

In the given example we simply have

$$h(t,\tau)=\delta(t/2-\tau)\tag{3}$$

For linear time-invariant (LTI) systems, $h(t,\tau)$ only depends on the difference $t-\tau$.