Intertwined evolution operators |
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Authors: | Wha-Suck?Lee Email author" target="_blank">Niko?SauerEmail author |
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Institution: | 1.Department of Mathematics and Applied Mathematics,University of Pretoria,Pretoria,South Africa;2.Centre for the Advancement of Scholarship,University of Pretoria,Pretoria,South Africa |
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Abstract: | We construct a convolution algebra of admissible homomorphisms defined on a ‘test space’ to demonstrate the fundamental role of convolution in the study of intertwined evolution operators of linear ordinary differential equations in Banach spaces and probability theory. The choice of test space makes the framework we present quite versatile. The applications include semigroups of linear operators, empathy, integrated semigroups and empathies and the convolution semigroups of probability theory. |
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