Anzeige
Erschienen in:
2001 | OriginalPaper | Buchkapitel
The Inhomogeneous Cauchy-Riemann Equation and Runge’s Theorem
verfasst von : Raghavan Narasimhan, Yves Nievergelt
Erschienen in: Complex Analysis in One Variable
Verlag: Birkhäuser Boston
Enthalten in: Professional Book Archive
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Holomorphic functions are characterized by the equation ∂É/∂z = 0. In this chapter, we shall study the equation ∂É/∂̄z = g when g has compact support. We shall obtain an explicit solution which leads to a variant of the Cauchy integral formula. This variant can often be used instead of the usual Cauchy formula, and has the advantage of not involving winding numbers. We shall illustrate this principle with a variant of the argument principle and a proof of the Runge theorem.