Making the case for Cauchy transforms
Making the case for Cauchy transforms
Making the case for Cauchy transforms
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(Kµ)(z) =<br />
=<br />
(1 − r)(Kµ)(re it ) =<br />
µ = c1δθ1 + c2δθ2 + · · · + cnδθn<br />
2π<br />
1<br />
0 1 − e−iθ z dµ(θ)<br />
c1 c2<br />
cn<br />
1 − e−iθ1z +<br />
1 − e−iθ2z + · · · +<br />
1 − e−iθnz (1 − r)c1<br />
1 − e<br />
(1 − r)c2<br />
(1 − r)cn<br />
−iθ1re<br />
+ it −iθ2re<br />
+ · · · + it −iθnreit 1 − e<br />
1 − e<br />
William T. Ross (University of Richmond) <strong>Making</strong> <strong>the</strong> <strong>case</strong> <strong>for</strong> <strong>Cauchy</strong> trans<strong>for</strong>ms 12 / 42