L1-estimates for eigenfunctions and heat kernel estimates for semigroups dominated by the free heat semigroup
نویسنده
چکیده
We investigate selfadjoint positivity preserving C0-semigroups that are dominated by the free heat semigroup on Rd. Major examples are semigroups generated by Dirichlet Laplacians on open subsets or by Schrödinger operators with absorption potentials. We show explicit global Gaussian upper bounds for the kernel that correctly reflect the exponential decay of the semigroup. For eigenfunctions of the generator that correspond to eigenvalues below the essential spectrum we prove estimates of their L1-norm in terms of the L2-norm and the eigenvalue counting function. This estimate is applied to a comparison of the heat content with the heat trace of the semigroup. MSC 2010: 35P99, 35K08, 35J10, 47A10
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