Tomoyo Kanazawa

A Direct Proof for an Eigenvalue Problem by Counting Lagrangian Submanifolds

Here we consider a kind of Schrödinger operators called the Bochner-Laplacian. Using Jensen's Formula and Vandermonde convolution, we show directly that for each $k=0,1,2,\ldots\,$, the number of Lagrangian submanifolds which satisfy the Maslov quantization condition is just equal to the multiplicity of the $k$th eigenvalue of the operator.

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University of Bialystok