Spectral functions of subordinate Brownian motion on closed manifolds:

2016 ◽  
Vol 93 (3) ◽  
pp. 703-720 ◽  
Author(s):  
M. A. Fahrenwaldt
Keyword(s):  
Brownian Motion ◽  
Spectral Functions ◽  
Subordinate Brownian Motion

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.

scholarly journals Minimal thinness for subordinate Brownian motion in half-space

2012 ◽  
Vol 62 (3) ◽  
pp. 1045-1080 ◽  
Author(s):  
Panki Kim ◽  
Renming Song ◽  
Zoran Vondraček
Keyword(s):  
Brownian Motion ◽  
Half Space ◽  
Subordinate Brownian Motion ◽  
Minimal Thinness
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