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Trotter-Kato product formula and fractional powers of self-adjoint generators

Authors:	Takashi Ichinose Valentin A Zagrebnov

Institution:	^a Department of Mathematics, Faculty of Science, Kanazawa University, Kanazawa 920-1192, Japan ^b Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Mohrenstrasse 39, D-210117 Berlin, Germany ^c Université de la Méditerranée (Aix-Marseille II) and CPT-CNRS-Luminy-Case 907, 13288 Marseille Cedex 9, France

Abstract:	Let A and B be non-negative self-adjoint operators in a Hilbert space such that their densely defined form sum obeys dom(H^α)⊆dom(A^α)∩dom(B^α) for some α∈(1/2,1). It is proved that if, in addition, A and B satisfy dom(A^1/2)⊆dom(B^1/2), then the symmetric and non-symmetric Trotter-Kato product formula converges in the operator norm: \|\|(e−tB/2ne−tA/ne−tB/2n)n−e−tH\|\|=O(n−(2α−1))\|\|(e−tA/ne−tB/n)n−e−tH\|\|=O(n−(2α−1))

Keywords:	Trotter-Kato product formula Operator norm convergence Fractional powers
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