On an integral transform by R. S. Phillips
Sten Bjon
Open Mathematics, Tome 8 (2010), p. 98-113 / Harvested from The Polish Digital Mathematics Library
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The properties of a transformation f↦f˜h by R.S. Phillips, which transforms an exponentially bounded C 0-semigroup of operators T(t) to a Yosida approximation depending on h, are studied. The set of exponentially bounded, continuous functions f: [0, ∞[→ E with values in a sequentially complete L c-embedded space E is closed under the transformation. It is shown that (f˜h)k˜=f˜h+k for certain complex h and k, and that f(t)=limh→0+f˜h(t) , where the limit is uniform in t on compact subsets of the positive real line. If f is Hölder-continuous at 0, then the limit is uniform on compact subsets of the non-negative real line. Inversion formulas for this transformation as well as for the Laplace transformation are derived. Transforms of certain semigroups of non-linear operators on a subset X of an L c-embedded space are studied through the C 0-semigroups, which they define by duality on a space of functions on X.

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:269503 
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     author = {Sten Bjon},
     title = {On an integral transform by R. S. Phillips},
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     volume = {8},
     year = {2010},
     pages = {98-113},
     zbl = {1202.44002},
     language = {en},
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Sten Bjon. On an integral transform by R. S. Phillips. Open Mathematics, Tome 8 (2010) pp. 98-113. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0058-8/

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