## Analysis on Unions of Intervals |

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analytic continuation analytic functions analytic on a,b Banach spaces Borel measure supported bounded intervals a,b bounded inverse bounded operators Cayley inner function Chapter 1 Bernstein's characterizing those sequences compact sets compact subset complex numbers complex vector space corresponds a unique define the function Ec.K equation exist a finite F defined f e H f is analytic finite positive Borel finite union function defined function F functional Hilbert space functions analytic Hausdorff's little Hence holds for a.e. holomorphic function integral transformation formula Lebesgue measure Let f limsup linear span linear transformation little moment problem Lp a,b measurable function polynomials positive Borel measure positive integer PROOF Proposition rational functions real line real numbers reproducing kernel Rovnyak sequence of complex sequence of real space H spectral mapping theorem spectral theorem theory of Cayley transformation formula Theorem union of closed unique r+1 unit circle unitary operators wj+k+2 Zc.K