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 Δ0⩽n−v+2 is obtained. It is also
proved that the quantity n−v+1−dim ker Δ0 cannot be
reduce while adding new edges and manifolds.