Making the case for Cauchy transforms
Making the case for Cauchy transforms
Making the case for Cauchy transforms
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
Theorem (<strong>Cauchy</strong> - 1831)<br />
If f is analytic on {|z| < 1} and continuous on {|z| 1}, <strong>the</strong>n<br />
f (z) =<br />
2π<br />
0<br />
f (eiθ )<br />
1 − e−iθ dθ<br />
z 2π .<br />
f (z) = 1<br />
<br />
f (ζ)<br />
2πi |ζ|=1 ζ − z dζ<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 4 / 42