caa a22 4500 467931909 CHVBK 20180406152945.0 cr unu---uuuuu 170328e20061201xx s 000 0 eng 10.1007/s00020-006-1433-5 doi (NATIONALLICENCE)springer-10.1007/s00020-006-1433-5 Xia Daoxing Department of Mathematics, Vanderbilt University, 37240, Nashville, TN, USA aut Determinant Formula for the Trace Class Perturbation of Heisenberg Commutation Relation [Elektronische Daten] [Daoxing Xia] Abstract.: In this paper we establish a determinant formula $$ \det {\left( {e^{{if(u)}} e^{{ig(v)}} e^{{ - if(u)}} e^{{ - ig(v + f'(u))}} } \right)} = e^{{itr{\left( {(g(v + f'(u)) - g(v))D} \right)}}} $$ for a pair of unbounded self-adjoint operators u and v satisfying a commutation relation $$ i{\left( {uv - vu} \right)} \subset I + D $$ where D is in the trace class, and some other condition. The functions f and g are rational functions satisfying certain condition. Birkhäuser Verlag, Basel, 2006 nationallicence Integral Equations and Operator Theory Birkhäuser-Verlag; http://www.birkhauser.ch 56/4(2006-12-01), 571-585 0378-620X 56:4<571 2006 56 20 https://doi.org/10.1007/s00020-006-1433-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00020-006-1433-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Xia Daoxing Department of Mathematics, Vanderbilt University, 37240, Nashville, TN, USA aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag; http://www.birkhauser.ch 56/4(2006-12-01), 571-585 0378-620X 56:4<571 2006 56 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer