Interpolation Theory

Advanced Topics in Shannon Sampling and Interpolation Theory is the second volume of a textbook on signal analysis solely devoted to the topic of sampling and restoration of continuous time signals and images. Sampling and reconstruction are fundamental problems in any field that deals with real-time signals or images, including communication engineering, image processing, seismology, speech recognition, and digital signal processing.

This book is the third edition of the 1999 lecture notes of the courses on interpolation theory that the author delivered at the Scuola Normale in 1998 and 1999.

1. Interpolation problems play an important role both in theoretical and applied investigations. This explains the great number of works dedicated to classical and new interpolation problems ([1)-[5], [8), [13)-[16], [26)-[30], [57]). In this book we use a method of operator identities for investigating interpo­ lation problems.

About one half of the papers in this volume are based on lectures which were pre­ sented at a conference at Leipzig University in August 1994, which was dedicated to Vladimir Petrovich Potapov.