Subnormal weighted translation semigroups |
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Authors: | Mary R Embry Alan Lambert |
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Institution: | Mathematics Department, The University of North Carolina, Charlotte, North Carolina 28223 USA |
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Abstract: | A weighted translation semigroup {St} on L2(+) is defined by for x ? t and 0 otherwise, where φ is a continuous nonzero scalar-valued function on +. It is shown that {St} is subnormal if and only if φ2 is the product of an exponential function and the Laplace-Stieltjes transform of an increasing function of total variation one. A necessary and sufficient condition for similarity of weighted translation semigroups is developed. |
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