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Remarks on the Trotter-Kato Product Formula for Unitary Groups
- 1.0365872 - ÚJF 2012 RIV CH eng J - Journal Article
Exner, Pavel - Neidhardt, H. - Zagrebnov, VA.
Remarks on the Trotter-Kato Product Formula for Unitary Groups.
Integral Equations and Operator Theory. Roč. 69, č. 4 (2011), s. 451-478. ISSN 0378-620X. E-ISSN 1420-8989
R&D Projects: GA MŠMT LC06002
Institutional research plan: CEZ:AV0Z10480505
Keywords : Trotter product formula * Trotter-Kato product formula * unitary groups
Subject RIV: BE - Theoretical Physics
Impact factor: 0.626, year: 2011
Let A and B be non-negative self-adjoint operators in a separable Hilbert space such that their form sum C is densely defined. It is shown that the Trotter product formula holds for imaginary parameter values in the L (2)-norm, that is, one has for each element h of the Hilbert space and any T > 0. This result is extended to the class of holomorphic Kato functions, to which the exponential function belongs. Moreover, for a class of admissible functions: where for any T > 0.
Permanent Link: http://hdl.handle.net/11104/0201015
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