Analytic Function Theory, Volume 1
Emphasizes the conceptual and historical continuity of analytic function theory. This book covers canonical topics including elliptic functions, entire and meromorphic functions, as well as conformal mapping. It also features chapters on majorization and on functions holomorphic in a half-plane.
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absolutely convergent algebra analytic angle asserted bounded BV[a Cauchy Cauchy-Riemann equations Cauchy's coefficients complex numbers complex plane continuous function convergent series converges uniformly corresponding defined definition denote derivative disk domain double series elements entire function equation EXERCISE exists finite number follows formula given half-plane HB[D Hence holomorphic function imaginary implies inequality infinite infinity integral interior intersection interval inverse Lemma limit point line segment logarithm mapping meromorphic function multiplication neighborhood obtain partial sums point z0 poles polynomial positive integer power series Problem properties prove radius of convergence rational function real axis real numbers rectifiable curve residue result Riemann roots scroc Section sequence series converges simple closed polygon singular point solution subset Suppose tangent tends to zero that/(z theorem theory triangle uniform convergence unique unit circle vector Verify z-plane
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Strongly Elliptic Systems and Boundary Integral Equations
William Charles Hector McLean
Limited preview - 2000