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- W3113940061 abstract "Let m ∈ N $min mathbb {N}$ , P ( D ) : = ∑ | α | = 2 m ( − 1 ) m a α D α $P(D):=sum _{|alpha |=2m}(-1)^m a_alpha D^alpha$ be a 2 m $2m$ -order homogeneous elliptic operator with real constant coefficients on R n $mathbb {R}^n$ , and V $V$ a real-valued measurable function on R n $mathbb {R}^n$ . In this article, the authors introduce a new generalized Schechter class concerning V $V$ and show that the higher order Schrödinger operator L : = P ( D ) + V $mathcal {L}:=P(D)+V$ possesses a heat kernel that satisfies the Gaussian upper bound and the Hölder regularity when V $V$ belongs to this new class. The Davies–Gaffney estimates for the associated semigroup and their local versions are also given. These results pave the way for many further studies on the analysis of L $mathcal {L}$ ." @default.
- W3113940061 created "2021-01-05" @default.
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- W3113940061 date "2022-05-05" @default.
- W3113940061 modified "2023-10-13" @default.
- W3113940061 title "Gaussian estimates for heat kernels of higher order Schrödinger operators with potentials in generalized Schechter classes" @default.
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- W3113940061 doi "https://doi.org/10.1112/jlms.12620" @default.
- W3113940061 hasPublicationYear "2022" @default.
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