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:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
