Smoothing effect for time-degenerate Schrödinger operators
نویسندگان
چکیده
In this paper we focus on the validity of some fundamental estimates for time-degenerate Schr\"{o}dinger-type operators. On one hand derive global homogeneous smoothing operators any order by means suitable comparison principles (that shall obtain here). other hand, prove weighted Strichartz-type Scrh\"{o}dinger and apply them to local well-posedness semilinear Cauchy problem. Most our results nondegenerate as well, recovering, in these cases, well-known standard results.
منابع مشابه
Ü Estimates for Time - Dependent Schrödinger Operators
It is well known that the local decay estimates (2) are useful in studying nonlinear Schrödinger equations (see [8, §XI.13], [11]). On the other hand little seems to be known when one replaces the free operator HQ by more general Hamiltonians (4) H = -A + V(x), even when the potential V is in C^°(R). Obviously, one has to assume that H has no bound states for an estimate like (2) to it M hold f...
متن کاملA remark on the Schrödinger smoothing effect
— We prove the equivalence between the smoothing effect for a Schrödinger operator and the decay of the associate spectral projectors. We give two applications to the Schrödinger operator in dimension one. Résumé. — On donne une caractérisation de l’effet régularisant pour un opérateur de Schrödinger par la décroissance de ses projecteurs spectraux. On en déduit deux applications à l’opérateur ...
متن کاملTime-dependent Scattering Theory for Schrödinger Operators on Scattering Manifolds *
We construct a time-dependent scattering theory for Schrödinger operators on a manifold M with asymptotically conic structure. We use the two-space scattering theory formalism, and a reference operator on a space of the form R×∂M , where ∂M is the boundary of M at infinity. We prove the existence and the completeness of the wave operators, and show that our scattering matrix is equivalent to th...
متن کاملConvergence of Schrödinger Operators
For a large class, containing the Kato class, of real-valued Radon measures m on R the operators −∆ + ε∆ + m in L(R, dx) tend to the operator −∆ +m in the norm resolvent sense, as ε tends to zero. If d ≤ 3 and a sequence (μn) of finite real-valued Radon measures on R converges to the finite real-valued Radon measure m weakly and, in addition, supn∈N μ ± n (R) < ∞, then the operators −∆ + ε∆ + μ...
متن کاملNumerical solution for one-dimensional independent of time Schrödinger Equation
In this paper, one of the numerical solution method of one- particle, one dimensional timeindependentSchrodinger equation are presented that allows one to obtain accurate bound state eigenvalues and functions for an arbitrary potential energy function V(x).For each case, we draw eigen functions versus the related reduced variable for the correspondingenergies. The paper ended with a comparison ...
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: Journal of Differential Equations
سال: 2021
ISSN: ['1090-2732', '0022-0396']
DOI: https://doi.org/10.1016/j.jde.2021.07.006