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Short Survey of Caratheodory Problem
Approximation Existence Theorem
4 other sections not shown
becomes bounded Caratheodory problem Cauchy sequence chain rule chapter class h coefficients continuous function continuous Hermitian positive corresponding countable set da(t defined domain eigenfunctions element entire function equivalent exists fact finite following relation Fourier series fractional-linear transform function of positive Fundamental Matrix Inequality h e G hence Hermitian positive function Hilbert space holomorphic holomorphic function implies informative block integral representation interval J J j-1 j-1 J J J-unitary Kovalishina Krein problem left hand side Lemma H Let us show m-square Mz(x n n n non-decreasing non-negative non-singular numbers obtain operator pair of positive polynomial matrix positive function s(x positive type possessing the property proof proved real axis resolvent matrix satisfies FMI satisfies the inequality scalar product solution of FMI space G strictly positive Theorem uniformly uniquely unit disc upper half-plane vector z z z z