We first prove that the realization A_{min} of A := div(Q∇) − V in L^{2}(R^{d}) with unbounded coefficients generates a symmetric sub-Markovian and ultracontractive semigroup on L^2(R^d) which coincides on L^2(R^d) ∩ C_{b}(R^d) with the minimal semigroup generated by a realization of A on C_b(R^d). Moreover, using time-dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernel of A and deduce some spectral properties of Amin in the case of polynomially and exponentially growing diffusion and potential coefficients.
General kernel estimates of Schrödinger-type operators with unbounded diffusion terms
Loredana Caso;Marianna Porfido;Abdelaziz Rhandi
2023-01-01
Abstract
We first prove that the realization A_{min} of A := div(Q∇) − V in L^{2}(R^{d}) with unbounded coefficients generates a symmetric sub-Markovian and ultracontractive semigroup on L^2(R^d) which coincides on L^2(R^d) ∩ C_{b}(R^d) with the minimal semigroup generated by a realization of A on C_b(R^d). Moreover, using time-dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernel of A and deduce some spectral properties of Amin in the case of polynomially and exponentially growing diffusion and potential coefficients.File in questo prodotto:
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