Singular Value Decomposition for Continuous Variables

say I have a $n\times n$ matrix $w_{ij}$. I can preform a singular value decomposition such that $w_{ij}=\sum_l \sum_n u_{il}\lambda_{ln}v_{nj}$ with $\lambda_{ln}$ diagonal. Now, is there such a generalization so that, given a function of two variables $w(\theta_1,\theta_2)$ such that $$w(\theta_1 ,\theta_2)=\int dy \int dx \,u(\theta_1 ,x) \, \lambda(x,y) \, v(\theta_2 ,y)$$ 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 $$\exp {\alpha \cos(\theta-\phi)}=\int\int dx \, dy \, u(\theta,x) \, \lambda(\alpha,x,y) \, v(\phi,y)$$ Thanks.

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