Elementary Theory of Analytic Functions of One Or Several Complex VariablesÉditions scientifiques Hermann., 1963 - 226 páginas The case of analytic functions of several variables, real or complex, is considered to allow to consider harmonic functions of two real variables as analytic functions and to review the existence theorem of solutions of a differential system in the case where the data are analyzed using the "raising factor method." In his mode of exposition of this classical subject, the author departs from traditional paths by dealing with the theory of formal entire series and the notion of abstract analytical space, usually called "Riemann surface." Questions of planar topology, essential when dealing with the Cauchy integral, are approached from a point of view slightly different from that of Ahlfors. Complete proofs are also given of all the statements of the text, treated in detail, in connection with the theory of differential forms. |
Contenido
Соруз MATH | 7 |
POWER SERIES IN ONE VARIABLE | 9 |
Formal power series | 11 |
Derechos de autor | |
Otras 24 secciones no mostradas
Otras ediciones - Ver todas
Elementary Theory of Analytic Functions of One Or Several Complex Variables Henri Cartan Vista previa limitada - 1995 |
Elementary Theory of Analytic Functions of One or Several Complex Variables Henri Cartan Vista previa limitada - 2013 |
Elementary Theory of Analytic Functions of One Or Several Complex Variables Henri Cartan Vista de fragmentos - 1973 |
Términos y frases comunes
analytic functions annulus b₁ branch of log centre chapter circle closed disc closed path coefficients compact subsets completes the proof complex manifold complex number complex variable connected open set consider constant contained continuous function converges normally coordinate deduce definition denotes derivative differentiable path differential form equal equation exists finite number follows formal power series formal series function f half-plane harmonic function holo holomorphic function identically zero integral formula inverse isomorphism Laurent expansion lemma Let f maximum modulus principle mean value property meromorphic function morphic necessary and sufficient neighbourhood normally convergent open disc oriented boundary point at infinity pole polynomial power series expansion primitive proposition proved punctured disc radius of convergence real axis real number real variables rectangle relation residue Riemann sphere Riemann surface right hand side satisfies sequence simply connected sufficient condition sufficiently small tends theorem topology transformation z₁ όχ