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Subnormal weighted translation semigroups
Authors:Mary R Embry  Alan Lambert
Institution:Mathematics Department, The University of North Carolina, Charlotte, North Carolina 28223 USA
Abstract:A weighted translation semigroup {St} on L2(R+) is defined by (Stf)(x) = (φ(x)φ(x ? t))f(x ? t) for x ? t and 0 otherwise, where φ is a continuous nonzero scalar-valued function on R+. 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.
Keywords:
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