Interpolation on sequences using holomorphic functions
by Hoi-Sang Kong
THESIS
1994
M.Phil. Mathematics
vii, 37 leaves ; 30 cm
Abstract
The main results of this thesis are as follows. For Blaschke sequence {Zn} let T{zn}:H∞ → l∞ be the evaluation (or interpolation) function on {zn}. We proved that if the range of T{zn} is closed, then {zn} must be an interpolating sequence. We also proved that if {zn} is a Blaschke sequence, then T{zn} is not a compact operator. Moreover if the range of T{zn} contains a lp(P>0) space, then the Blaschke sequence {zn} is an interpolating sequence. We also discussed other functional analytical aspects of the operator T{zn}.
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