On the concavity of the surface of eigenvalues (Q1274076)

Let \(A\) be semibounded self-adjoint operator acting in a Hilbert space \(H\). The author proves that if \(A\) linearly depends on \(n\) real parameters and if its lowest spectral point is an isolated nondegenerate eigenvalue, then this eigenvalue is a concave function of the above parameters. For \(H = L_2({\mathbb R}^k)\) this result is generalized to a special class of operators that depend nonlinearly on numerical parameters.