Say, I have an $n\times n$ matrix $w_{ij}$. I can perform a singular value decomposition such that
$$ w_{ij}=\sum_l \sum_n u_{il}\lambda_{ln}v_{jn} $$
with $\lambda_{ln}$ diagonal. Now, is there such a generalization so that, given a function of two variables $w(\theta_1, \theta_2)$,
$$ w(\theta_1 ,\theta_2)=\int dy \int dx \,u(\theta_1 ,x) \, \lambda(x,y) \, v(\theta_2 ,y) $$
where $\lambda$ plays a similar role like it did in the SVD? For instance, say I have the following
$$ \exp {[\alpha \cos(\theta-\phi)]} $$
is it possible to find a decomposition such that
$$ \exp {\alpha \cos(\theta-\phi)}=\iint dx \, dy \, u(\theta,x) \, \lambda(\alpha,x,y) \, v(\phi,y) $$