On the generalized Ornstein-Uhlenbeck operators perturbed by regular potentials and inverse square potentials in weighted L²-spaces
نویسندگان
چکیده
Generation of a quasi-contractive semigroup by generalized Ornstein-Uhlenbeck operators ℒ = −∆ + ∇Φ · ∇ − G V c|x|−2 in the weighted space L2(RN, e−Φ(x)dx) is proven, where Φ ∈ C2(RN, R), C1(RN, RN), 0 ≤ C1(RN) and c > 0. The proofs are carried out an application L2-weighted Hardy inequality bilinear form techniques.
منابع مشابه
On Schrödinger Operators with Multipolar Inverse-square Potentials
Positivity, essential self-adjointness, and spectral properties of a class of Schrödinger operators with multipolar inverse-square potentials are discussed. In particular a necessary and sufficient condition on the masses of singularities for the existence of at least a configuration of poles ensuring the positivity of the associated quadratic form is established.
متن کاملOn Schrödinger Operators with Multisingular Inverse-square Anisotropic Potentials
We study positivity, localization of binding and essential self-adjointness properties of a class of Schrödinger operators with many anisotropic inverse square singularities, including the case of multiple dipole potentials.
متن کاملcompactifications and function spaces on weighted semigruops
chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...
15 صفحه اولThe generalized Ornstein–Uhlenbeck process
Langevin-like equations have been studied in the presence of arbitrary noise. The characteristic functional of the generalized Langevin process has been built up. Exact results for all cumulants are given. Particular stress has been put on the Campbell, dichotomous and radioactive decay noises. Transient relaxation, susceptibility and diffusion constants for different (noisy) media have been sk...
متن کاملMultivariate Generalized Ornstein-Uhlenbeck Processes
De Haan and Karandikar [12] introduced generalized Ornstein–Uhlenbeck processes as one-dimensional processes (Vt)t≥0 which are basically characterized by the fact that for each h > 0 the equidistantly sampled process (Vnh)n∈N0 satisfies the random recurrence equation Vnh = A(n−1)h,nhV(n−1)h + B(n−1)h,nh, n ∈ N, where (A(n−1)h,nh, B(n−1)h,nh)n∈N is an i.i.d. sequence with positive A0,h for each ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proyecciones
سال: 2022
ISSN: ['0716-0917', '0717-6279']
DOI: https://doi.org/10.22199/issn.0717-6279-5290