scholarly journals Error bounds on the Trotter-Kato product formula of relativistic Schrödinger operators with electromagnetic fields

2000 ◽  
Vol 76 (2) ◽  
pp. 7-12
Author(s):  
Atsushi Doumeki
Keyword(s):  
Electromagnetic Fields ◽  
Error Bounds ◽  
Schrödinger Operators ◽  
Product Formula ◽  
Schrodinger Operators ◽  
Relativistic Schrödinger Operators

scholarly journals The norm estimate of the difference between the Kac operator and the Schrödinger semigroup: A unified approach to the nonrelativistic and relativistic cases

1998 ◽  
Vol 149 ◽  
pp. 53-81 ◽  
Author(s):  
Takashi Ichinose ◽  
Satoshi Takanobu
Keyword(s):  
Schrödinger Operators ◽  
Product Formula ◽  
Operator Norm ◽  
Schrodinger Operators ◽  
Unified Approach ◽  
Trotter Product Formula ◽  
Nonrelativistic Case ◽  
Norm Estimate ◽  
Schrödinger Semigroup ◽  
The Difference

Abstract.An Lp operator norm estimate of the difference between the Kac operator and the Schrödinger semigroup is proved and used to give a variant of the Trotter product formula for Schrödinger operators in the Lp operator norm. The method of the proof is probabilistic based on the Feynman-Kac formula. The problem is discussed in the relativistic as well as nonrelativistic case.

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