Venue
LH 301
Speaker
Dr. Sumit Mohanty
Affiliation
IIT Kanpur
Title
Maximization of Combinatorial Schrodinger Operator's Smallest Eigenvalue with Dirichlet Boundary Condition
For a nonnegative potential function q and a given locally finite graph G, we study thecombinatorial Schr¨odinger operator Lq(G) = ∆G + q with Dirichlet boundary condition on aproper finite subset S of the vertex set of G such that the induced subgraph on S is connected.Let Υp = {q ∈ Lp(S) : q(x) ≥ 0, Px ∈Sqp(x) ≤ 1}, for 1 ≤ p < ∞. We prove the existenceand uniqueness of the maximizer of the smallest Dirichlet eigenvalue of Lq(G), whenever thepotential function q ∈ Υp. Furthermore, we also establish the analogue of the Euler-Lagrangeequation on graphs.