Heat Kernel Estimates and L P Spectral Independence of Elliptic Operators
Peer Christian Kunstmann · Bulletin of the London Mathematical Society · 1999
Let Ω be an open subset of Rd, and let Tp for p∈[1, ∞) be consistent C0-semigroups given by kernels that satisfy an upper heat kernel estimate. Denoting their generators by Ap, we show that the spectrum σ(Ap) is independent of p∈[1, ∞). We also treat the case of weighted Lp-spaces for weights that satisfy a subexponential growth condition. An example shows that independence of the spectrum may fail for an exponential weight. 1991 Mathematics Subject Classification 47D06, 47A10, 35P05.