Higher-order Kato class potentials for Schrödinger operators

2009 ◽  
Vol 41 (2) ◽  
pp. 293-301 ◽  
Author(s):  
Quan Zheng ◽  
Xiaohua Yao
Keyword(s):  
Schrödinger Operators ◽  
Higher Order ◽  
Schrodinger Operators ◽  
Kato Class

scholarly journals Long range scattering for higher order Schrödinger operators

2013 ◽  
Vol 254 (8) ◽  
pp. 3329-3351 ◽  
Author(s):  
Zhiwen Duan ◽  
Quan Zheng ◽  
Jing Feng
Keyword(s):  
Long Range ◽  
Schrödinger Operators ◽  
Higher Order ◽  
Schrodinger Operators

scholarly journals Higher order eigenvalues for non-local Schrödinger operators

2018 ◽  
Vol 17 (1) ◽  
pp. 191-208 ◽  
Author(s):  
Niels Jacob ◽  
◽  
Feng-Yu Wang ◽  
◽  
Keyword(s):  
Schrödinger Operators ◽  
Higher Order ◽  
Schrodinger Operators ◽  
Non Local

scholarly journals PATH INTEGRAL REPRESENTATION FOR SCHRÖDINGER OPERATORS WITH BERNSTEIN FUNCTIONS OF THE LAPLACIAN

2012 ◽  
Vol 24 (06) ◽  
pp. 1250013 ◽  
Author(s):  
FUMIO HIROSHIMA ◽  
TAKASHI ICHINOSE ◽  
JÓZSEF LŐRINCZI
Keyword(s):  
Brownian Motion ◽  
Path Integral ◽  
Schrödinger Operators ◽  
Integral Representations ◽  
Schrodinger Operators ◽  
Kato Class ◽  
Path Integral Representation ◽  
Bernstein Functions ◽  
Subordinate Brownian Motion ◽  
The One

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 subordinate Brownian motion. As specific examples, fractional and relativistic Schrödinger operators with magnetic field and spin are covered. Results on self-adjointness of these operators are obtained under conditions allowing for singular magnetic fields and singular external potentials as well as arbitrary integer and half-integer spin values. This approach also allows to propose a notion of generalized Kato class for which an Lp-Lq bound of the associated generalized Schrödinger semigroup is shown. As a consequence, diamagnetic and energy comparison inequalities are also derived.

L estimates for fractional Schrödinger operators with Kato class potentials

2018 ◽  
Vol 265 (9) ◽  
pp. 4181-4212 ◽  
Author(s):  
Shanlin Huang ◽  
Ming Wang ◽  
Quan Zheng ◽  
Zhiwen Duan
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Kato Class
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