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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

3 votes
2 answers
134 views

series representation of bivariate functions

Given a bivariate function $f(x, y)$ with $x \in [-a,a]$ and $y \in [-b, b]$, what is the necessary and sufficient condition under which we can write $f(x, y) = \sum g_k(x)h_k(y)$ for all $(x,y)$ in t …
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