Elementary Theory of Analytic Functions of One Or Several Complex Variables
Noted mathematician offers basic treatment of theory of analytic functions of a complex variable, touching on analytic functions of several real or complex variables as well as the existence theorem for solutions of differential systems where data is analytic. Also included is a systematic, though elementary, exposition of theory of abstract complex manifolds of one complex dimension. Topics include power series in one variable, holomorphic functions, Cauchy’s integral, more. Exercises. 1973 edition.
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Elementary Theory of Analytic Functions of One or Several Complex Variables
Limited preview - 2013
analytic functions automorphism centre chapter circle closed disc closed path coefﬁcients coeﬁicients compact subsets completes the proof complex manifold complex manifold structure complex number complex variable condition connected open set consider constant contained continuous function converges normally converges uniformly coordinate deduce deﬁned Deﬁnition denotes differential form equal exists f is holomorphic ﬁeld ﬁnd ﬁnite number ﬁrst ﬁxed follows formal power series formal series function deﬁned function f half-plane harmonic function holo holomorphic function holomorphic mapping homeomorphism identically zero inverse isomorphism lemma Let f maximum modulus principle mean value property meromorphic function morphic neighbourhood normally convergent open disc oriented boundary point at inﬁnity pole polynomial power series expansion primitive proposition proved radius of convergence real axis real number rectangle relation residue Riemann sphere Riemann surface right hand side satisﬁes sequence simple simply connected space sufﬁciently tends theory topology transformation unique unit disc