A Direct Proof for an Eigenvalue Problem by Counting Lagrangian Submanifolds
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We focus on one of the Schrödinger operators called the Bochner– Laplacian. Using Jensen’s Formula and Vandermonde convolution, we show directly that for each k = 0, 1, 2, . . . , the number of Lagrangian submanifolds which satisfy the Maslov quantization condition is just equal to the multiplicity of the kth eigenvalue of the operator.
KeywordsJensen’s Formula Vandermonde convolution Bochner–Laplacian
Mathematics Subject Classification (2000)Primary 05A10 Secondary 53D12
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