The Schwarz Function and Its Applications

Philip J. Davis

ISBN 10: 088385046X / ISBN 13: 9780883850466

Published by Mathematical Association Of America Dez 1974, 1974

About this Item

Neuware - One of the principles of mathematical growth is that the relabelling process often suggests a new generation of problems. Means become ends; the medium rapidly becomes the message. This book is not wholly self-contained. Readers will find that they should be familiar with the elementary portions of linear algebra and of the theory of functions of a complex variable.

Seller Inventory # 9780883850466

Bibliographic Details

• Title: The Schwarz Function and Its Applications
• Publisher: Mathematical Association Of America Dez 1974
• Publication Date: 1974
• Language: English
• ISBN 10: 088385046X
• ISBN 13: 9780883850466
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 229W x 152H x 0D millimeters 229 millimeters width by 152 millimeters height by 0 millimeters depth
• Weight: 330 grams

About this title

Synopsis

H. A. Schwarz showed us how to extend the notion of reflection in straight lines and circles to reflection in an arbitrary analytic arc. Notable applications were made to the symmetry principle and to problems of analytic continuation. Reflection, in the hands of Schwarz, is an antianalytic mapping. By taking its complex conjugate, we arrive at an analytic function that we have called here the Schwarz Function of the analytic arc. This function is worthy of study in its own right and this essay presents such a study. In dealing with certain familiar topics, the use of the Schwarz Function lends a point of view, a clarity and elegance, and a degree of generality which might otherwise be missing. It opens up a line of inquiry which has yielded numerous interesting things in complex variables; it illuminates some functional equations and a variety of iterations which interest the numerical analyst. The perceptive reader will certainly find here some old wine in relabelled bottles. But one of the principles of mathematical growth is that the relabelling process often suggests a new generation of problems. Means become ends; the medium rapidly becomes the message. This book is not wholly self-contained. Readers will find that they should be familiar with the elementary portions of linear algebra and of the theory of functions of a complex variable.