Principles of Analysis

Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles.

The tread of this book is formed by two fundamental principles of Harmonic Analysis: the Plancherel Formula and the Poisson S- mation Formula. We ?rst prove both for locally compact abelian groups.

Program analysis concerns static techniques for computing reliable approximate information about the dynamic behaviour of programs. Applications include compilers (for code improvement), software validation (for detecting errors in algorithms or breaches of security) and transformations between data representation (for solving problems such as the Y2K problem).