Display that supports full CIE xyY color space Right now, all current monitors use three (or four) primary colors to create their color, which could never allow them to produce all colors that can be seen by the human eye; in fact, their colors will always be inside a triangle on the xyY diagram of all possible colors.

But we could decide to replace these color filters with something such as Lyot filters, which can be tuned, similarly to LCDs, to allow only light whose wavelength is higher/lower than a certain value to pass through. 

This would mean that we could basically create color filters that can be adjusted to produce any color, by replacing each pixel with two stacked filters, which allow a range $[a, b]$ to pass, and a third filter next to it which allows the range $[c,\infty)$ to pass through.

Using Mathematica, I have tested that a mapping between these three values is enough to create any possible $x$, $y$ and $Y$ in the CIE xyY color space:



So, in other words, the range of 
$$\text{XYZ}(a,b,c)=\int_{[a,b]\cup[c,\infty)}\text{I}(\lambda)\cdot(\overline{x}(\lambda),\overline{y}(\lambda),\overline{z}(\lambda))$$

, where $\text{I}$ is the illuminant, is enough to produce the color of any object that can be illuminated by that illuminant.

So, my questions are: 


Are there already any such displays that can produce any visible color, and if not, then why not?
Could this actually be done in practice?
No, most likely these kinds of displays do not exist, at the time of writing this post. Although the negative is hard to prove. And in this case i don't have deep enough understanding of the lore.

Reason for me saying this is that usable displays need some serious miniaturization. The miniaturization process is quite expensive and requires some serious investment. There should be quite massive patent trail if this was indeed true. So we should look in patent databases for this trail.

Second, having such tech probably will not yield full color space, at least initially. Because the filter can only filter out colors that the back light can generate. Most probably therefore this is some kind of projector technology at first. Also filters probably have a practical limit to how much they can be tuned.

Third, if/when such tech is available it must recuperate the development cost by selling enough units to overcome the capital investment. There is a likelihood that this is one of those things that can not be produced without the miniaturization step like digital cameras. So keep a lookout for a killer application for this tech.

Some major downsides of this kind of tech is the fact that you filter out light. This means it eats up part of the energy input. This leads to a heat dissipation problem, which for perfect narrow band filters is actually pretty huge part of the emitted light. Lot of energy goes wasted, and needs to be engineered around.