Abstract:
For the Laplace–Beltrami operator (the operator is given by a
Lagrangian plane $\Lambda$ ), an isomorphism between the its kernel
and intersection of $\Lambda$ and fixed lagrangian plane is described.
For the $\Delta^0$ operator with “continuity” conditions (on a
connected finite graph with $n$ edges and $v$ vertices), the
inequality $\dim$ ker $\Delta^0 \le n - v + 2$ is obtained. It is also
proved that the quantity $n - v + 1 - \dim$ ker $\Delta^0$ cannot be
reduce while adding new edges and manifolds.
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