The spectral function and principal eigenvalues for Schrodinger operators

Let m ∈ L1 loc (ℝN), 0 ≠ m+ in Kato's class. We investigate the spectral function λ rarr; s(Δ + λm) where s(Δ + λm) denotes the upper bound of the spectrum of the Schrödinger operator Δ + λm. In particular, we determine its derivative at 0. If m- is sufficiently large, we show that there exists...