Free membrane eigenvalues

For a simply connected and normalized domain D in the plane it was proven by Pólya and Schiffer in 1954 for the fixed membrane eigenvalues

?n1 \frac1lj 3 ?n1 \frac1l(0)j\sum \limits^{n}_{1} \frac{1}{{\lambda}_j} \geq \sum \limits^{n}_{1} \frac{1}{{\lambda}^{(0)}_j}
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