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Differential operators on singular spaces, algebraically integrable systems and quantization
October 24, 2016 18:30–20:00, Moscow
 


The kernel of the Laplace–Beltrami operator on a decorated graph

A. A. Tolchennikov

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Abstract: For the Laplace–Beltrami operator (the operator is given by a Lagrangian plane Λ ), an isomorphism between the its kernel and intersection of Λ and fixed lagrangian plane is described. For the Δ0 operator with “continuity” conditions (on a connected finite graph with n edges and v vertices), the inequality dim ker Δ0nv+2 is obtained. It is also proved that the quantity nv+1dim ker Δ0 cannot be reduce while adding new edges and manifolds.
 
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