2026-03-11T04:51:11Z https://kanazawa-u.repo.nii.ac.jp/oai

oai:kanazawa-u.repo.nii.ac.jp:00010551 2024-06-20T06:06:42Z 934:935:937

Path integral representation for schrödinger operators with bernstein functions of the laplacian 廣島, 文生 一瀬, 孝 Hiroshima, Fumio 796 00330358 00330358 Ichinose, Takashi 15115 20024044 20024044 Lörinczi, József 16008 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 FeynmanKac 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 L p-L q bound of the associated generalized Schrödinger semigroup is shown. As a consequence, diamagnetic and energy comparison inequalities are also derived. © 2012 World Scientific Publishing Company. journal article World Scientific Publishing 2012-07-01 AM application/pdf Reviews in Mathematical Physics 6 24 1250013 AA10723815 0129-055X https://kanazawa-u.repo.nii.ac.jp/record/10551/files/SC-PR-ICHINOSE-T-1250013.pdf https://doi.org/10.24517/00010538 http://hdl.handle.net/2297/31976 https://kanazawa-u.repo.nii.ac.jp/records/10551 eng 10.1142/S0129055X12500134