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I am interested in the bounding the Fourier coefficients $a_{m,n}$ of the function $f(x,y)=\sqrt{x^2+y^2}$ defined on the interval $[-1,1]^2$. I am specifically interested in understanding the behavior of the coefficients asymptotically in terms of $m,n\in\mathbb{Z}$. I attempted to consider the explicit expression for the Fourier coefficients but the integrals involving $f(x,y)$ become nontrivial to evaluate. Any suggestions?

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How do you define $a_{m,n}$? – Norbert Aug 1 '12 at 19:51

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