Are there any orthonormal bases for strictly convex functions $f: \mathbb{R}^n\ni x \mapsto \mathbb{R},\ x\ne y\implies f\left(\alpha x+\left(1-\alpha\right)y\right) \lt \alpha f(x)+(1-\alpha)f(y) \wedge \alpha\in(0,1)$?

The subset of $\mathbb{R}^n$ on which $f$ is defined can be restricted in any appropriate way e.g. unit cube, unit sphere, etc.