Reference : Evolution semigroups and time operators on Banach spaces
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Evolution semigroups and time operators on Banach spaces
Suchanecki, Zdzislaw mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >]
Gomez-Cubillo, Fernando [Institute of Mathematics and Informatics, Poland]
Journal of Mathematical Analysis and Applications
[en] Innovation ; Time operator ; Banach space ; Schauder basis
[en] We present new general methods to obtain shift representation of evolution semigroups defined on Banach spaces. We introduce the notion of time operator associated with a generalized shift on a Banach space and give some conditions under which time operators can be defined on an arbitrary Banach space. We also tackle the problem of scaling of time operators and obtain a general result about the existence of time operators on Banach spaces satisfying some geometric conditions. The last part of the paper contains some examples of explicit constructions of time operators on function spaces.

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