6533b838fe1ef96bd12a468c

RESEARCH PRODUCT

Evolution semigroups and time operators on Banach spaces

Zdzislaw SuchaneckiFernando Gómez-cubillo

subject

Unbounded operatorMathematics::Functional AnalysisBanach spaceSchauder basisApproximation propertyNuclear operatorApplied MathematicsTime operatorFinite-rank operatorBanach manifoldOperator theoryAlgebraInterpolation spaceC0-semigroupInnovationAnalysisMathematicsMathematicsofComputing_DISCRETEMATHEMATICS

description

AbstractWe 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.

yearjournalcountryeditionlanguage
2010-11-01Journal of Mathematical Analysis and Applications
10.1016/j.jmaa.2010.05.049http://dx.doi.org/10.1016/j.jmaa.2010.05.049