A pr 2 01 6 Kato ’ s Inequality for Magnetic Relativistic Schrödinger Operators
نویسندگان
چکیده
Kato’s inequality is shown for the magnetic relativistic Schrödinger operator HA,m defined as the operator theoretical square root of the selfadjoint, magnetic nonrelativistic Schrödinger operator (−i∇−A(x))2 +m2 with an Lloc vector potential A(x). Mathematics Subject Classification (2010): 47A50; 81Q10; 47B25; 47N50; 47D06; 47D08.
منابع مشابه
Probabilistic Representation and Fall-Off of Bound States of Relativistic Schrödinger Operators with Spin 1/2
A Feynman-Kac type formula of relativistic Schrödinger operators with unbounded vector potential and spin 1/2 is given in terms of a three-component process consisting of Brownian motion, a Poisson process and a subordinator. This formula is obtained for unbounded magnetic fields and magnetic field with zeros. From this formula an energy comparison inequality is derived. Spatial decay of bound ...
متن کاملHardy-lieb-thirring Inequalities for Fractional Schrödinger Operators
We show that the Lieb-Thirring inequalities on moments of negative eigenvalues of Schrödinger-like operators remain true, with possibly different constants, when the critical Hardy-weight C|x|−2 is subtracted from the Laplace operator. We do so by first establishing a Sobolev inequality for such operators. Similar results are true for fractional powers of the Laplacian and the Hardy-weight and,...
متن کامل1 6 M ay 2 00 6 Generalized 3 G theorem and application to relativistic stable process on non - smooth open sets
Let G(x, y) and GD(x, y) be the Green functions of rotationally invariant symmetric αstable process in R and in an open set D respectively, where 0 < α < 2. The inequality GD(x, y)GD(y, z)/GD(x, z) ≤ c(G(x, y) + G(y, z)) is a very useful tool in studying (local) Schrödinger operators. When the above inequality is true with c = c(D) ∈ (0,∞), then we say that the 3G theorem holds in D. In this pa...
متن کاملPath Integral Representation for Schrödinger Operators with Bernstein Functions of the Laplacian
Path integral representations for generalized Schrödinger operators obtained under a class of Bernstein functions of the Laplacian are established. The one-to-one correspondence of Bernstein functions with Lévy subordinators is used, thereby the role of Brownian motion entering the standard Feynman-Kac formula is taken here by subordinated Brownian motion. As specific examples, fractional and r...
متن کاملProgram of a Mini - Course “ Resonances and Threshold Singularities for Magnetic Quantum Hamiltonians ”
1. Basic facts from the spectral theory of magnetic quantum Hamilto-nians (Schrödinger, Pauli, and Dirac operators with magnetic fields): self-adjointness, gauge invariance, diamagnetic inequality, Aharonov-Casher theorem [1, 7]. Constant magnetic fields [1]. 2. Berezin-Toeplitz operators and pseudodifferential operators with con-4. Resonances for the 3D Schrödinger operator with constant magne...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016