Problems in Real and Functional Analysis

This book is another in the great tradition of problem books in analysis that trace its origins back to Pólya and Szegő’s Aufgaben und Lehrsätze aus der Analysis, better known in translation as Problems and Theorems in Analysis and which has included well-known classics by Paul Halmos, Gelbaum, Olmstead as well as many others.

The book is an extensive collection of problems in graduate real and functional analysis. It would be a great supplement to graduate courses in these areas and for graduate students preparing for qualifying exams. The book is divided into two major parts with the first half containing the problems and the second half solutions to about two-thirds of them. Many of the problems are posed in an open-ended invitation to research-type fashion. Each chapter is prefaced by a brief overview of the topics and important references.

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Steven Deckelman is a professor of mathematics at the University of Wisconsin-Stout, where he has been since 1997. He received his Ph.D from the University of Wisconsin-Madison in 1994 for a thesis in several complex variables written under Patrick Ahern. Some of his interests include complex analysis, mathematical biology and the history of mathematics.