Inner multipliers of de Branges's spaces |
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Authors: | Benjamin A Lotto |
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Institution: | (1) Department of Mathematics, Michigan State University, Wells Hall, 48823 East Lansing, MI |
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Abstract: | For a given functionb in the unit ball ofH
and an arbitraryH
functionm, the question of whenm is a multiplier of the de Branges space
(that is, when
is invariant under multiplication bym) is examined. Some necessary and sufficient conditions thatm be a multiplier of
are found and it is shown that there are no nonconstant inner multipliers of
whenb is a nonconstant extreme point of the unit ball ofH
. A new proof is given of the known fact that
is invariant under multiplication byz whenb is not an extreme point of the unit ball ofH
. Finally, we give a new proof of the known fact that an inner functionm is a multiplier of
forb(z)=(1+z)/2 if and only ifm belongs to the range of
.Some of the work in this paper originally appeared in the author's doctoral disseratation written at the University of California at Berkeley under the supervision of Donald Sarason. |
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Keywords: | |
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