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We prove the existence of an open set $\Omega\subset\mathbb{S}^2$ for which the first positive eigenvalue of the Laplacian with Neumann boundary condition exceeds that of the geodesic disk having the same area. This exam...
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This note contains below topics, for each integrable f, FOURIER COEFFICIENTS, BASIC PROPERTIES, FOURIER SERIES, SUMMABILITY IN NORM....