Construction of non-linear semi-groups using product formulas |
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Authors: | Fred B Weissler |
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Institution: | (1) Department of Mathematics, The University of Texas, 78712 Austin, Texas, USA |
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Abstract: | Under certain circumstances, the Trotter-Lie formulaW
t=lim(U
t/nVt/n)
n
is used to construct a non-linear semi-groupW
t on closed subsets ofL
P, 1≦p<∞. In particular we consider the situation whereU
t=e
tA is a positivity preservingC
0 (linear) semi-group andV
t is generated by a (non-linear) functionF with certain monotonicity properties. In general,A andF are “singular” onL
p and no requirement is made that one of them be “relatively bounded” with respect to the other. The generator of the resulting
semi-groupW
t turns out to be an extension ofA +F restricted to a suitable domain.
Research supported by a Danforth Graduate Fellowship and a Weizmann Postdoctoral Fellowship. |
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Keywords: | |
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