I am currently going through the CBMM course on statistical learning theory. Towards the end of their class on Reproducing Kernel Hilbert Spaces, the lecturer gives the following hypothesis set as an example.
$$ \mathcal{H} = \{ f \: | \: \forall w \in \mathbb{R}, \: \hat{f}(w) \in \; [-\gamma, \gamma]\}, \quad 0 < \gamma < \infty $$
The lecturer then discusses the Reproducing Kernel for $\mathcal{H}$.
The lecturer seems to imply that such a hypothesis set is limited in the sense that each function in the set is bounded in terms of frequency. In other words, the set contains functions that have bounded support in the Fourier domain and that functions can only be composed of frequencies within a given interval, specified via $\gamma$.
From my limited understanding of Fourier Transforms, it seems to me that the membership condition on $\mathcal{H}$ is simply saying that no component frequency can "form" too much of the function. In other words, each function in $\mathcal{H}$ can only contain "so much" of frequency $w$. So my question is, how should I interpret the membership condition on $\mathcal{H}$? Should I think of it as eliminating all functions that contain frequencies outside the window specified by $\gamma$, or as eliminating functions which are dominated by a single component frequency? I have limited experience with the Fourier Transform, only having really seen it in the context of Computer Vision tasks, so I assuming that my misunderstanding may be down to this.