Row Convergence of Algebraic Approximations

✍ Scribed by A.W. Mcinnes; T.H. Marshall

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 657 KB
• Volume: 75
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1993.1089

✦ Synopsis

An (\mathbf{n}) algebraic function of degree (p) satisfies an algebraic equation of degree (p), whose polynomial coefficients have maximum degrees given by the vector (\mathbf{n}). If a function which is analytic at the origin is approximated by an (\mathbf{n}) algebraic function of degree (p), the table of approximations is a table of dimension (p+1). Under suitable conditions, the sequence of algebraic approximations along an arbitrary "row" (a line parallel to an arbitrary axis in the table) converges to a given meromorphic function, unitformly on a suitable compact set. 1993 Academic Press, Inc.