As a guideline for the syllabus in this course we will refer to the book "Topics in Real and Functional Analysis" by Gerald Teschl. A pdf-version of this book can be downloaded here.
As in the previous years, the syllabus will consist of large parts of chapters 1, 2, 3, 5, 7 and 8 in Teschl's book. In addition, we will cover some Fourier analysis.
Concerning the material on Banach spaces, Hilbert spaces and operators (from chapters 1, 2, 3 and 5 in Teschl's book), we will mainly follow the book "Linear Functional Analysis" (second edition) by Bryan R. Rynne and Martin A. Youngson, Springer Undergraduate Mathematics Series, ISBN 978-1-84800-004-9. This book is more easily accessible than Teschl's book and contains many exercises (with solutions). Relevant chapters are 1, 2, 3, 4, 6, 7 and 8, but we will probably not have time to cover every topics in these chapters.
Most of the material on measure and integration theory (from chapters 7 and 8 in Teschl's book) is also covered in chapters 5 and 6 of Tom Lindstr?m's notes for MAT2400 (spring 2013). These chapters can be downloaded here .