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Title: Path integral representation for Schrödinger operators with Bernstein Functions of the Laplacian
Authors: Hiroshima, Fumio
Ichinose, Takashi
Lorinczi, Jozsef
Keywords: Feynman-Kac formula
Generalized Schrodinger operator
Bernstein function
Levy process
Poisson process
Heat semigroup
Issue Date: 2012
Publisher: © World Scientific Publishing Co Pte Ltd
Citation: HIROSHIMA, F., ICHINOSE, T. and LORINCZI, J., 2012. Path integral representation for Schrödinger operators with Bernstein Functions of the Laplacian. Reviews in Mathematical Physics, 24 (1250013), 40pp.
Abstract: 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.
Description: Electronic version of an article published by World Scientific Publishing Company at: http://dx.doi.org/10.1142/S0129055X12500134
Version: Accepted for publication
DOI: 10.1142/S0129055X12500134
URI: https://dspace.lboro.ac.uk/2134/21957
Publisher Link: http://dx.doi.org/10.1142/S0129055X12500134
ISSN: 0129-055X
Appears in Collections:Published Articles (Maths)

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