抄録
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.
| 元の言語 | 英語 |
|---|---|
| 記事番号 | 1250013 |
| ジャーナル | Reviews in Mathematical Physics |
| 巻 | 24 |
| 発行部数 | 6 |
| DOI | |
| 出版物ステータス | 出版済み - 7 1 2012 |
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All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
これを引用
Path integral representation for schrödinger operators with bernstein functions of the laplacian. / Hiroshima, Fumio; Ichinose, Takashi; Lrinczi, József.
：: Reviews in Mathematical Physics, 巻 24, 番号 6, 1250013, 01.07.2012.研究成果: ジャーナルへの寄稿 › 記事
}
TY - JOUR
T1 - Path integral representation for schrödinger operators with bernstein functions of the laplacian
AU - Hiroshima, Fumio
AU - Ichinose, Takashi
AU - Lrinczi, József
PY - 2012/7/1
Y1 - 2012/7/1
N2 - 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.
AB - 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.
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UR - http://www.scopus.com/inward/citedby.url?scp=84862563972&partnerID=8YFLogxK
U2 - 10.1142/S0129055X12500134
DO - 10.1142/S0129055X12500134
M3 - Article
VL - 24
JO - Reviews in Mathematical Physics
JF - Reviews in Mathematical Physics
SN - 0129-055X
IS - 6
M1 - 1250013
ER -