We know that in the space of functions, its possible to find a complete set so that you can write for an arbitrary function f, ## f(x)=\sum_n a_n \phi_n(x) ## and use the orthonormality relations between ## \phi##s to find the coefficients.(adsbygoogle = window.adsbygoogle || []).push({});

But is it possible to find a set of functions ## \phi_n(x,y) ## such that you can write for an arbitrary function of x and y ## f(x,y)=\sum_n c_n \phi_n(x,y) ##? Is there any orthonormality relation that lets you find the coefficients?

Thanks

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# Complete set of multi-variable functions

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