Fourier analysis.

Author: (USA) Loukas Grafakos
Publisher:
Publish Date: 2006-01-01
Features: The Fourier transform is a very useful method in digital signal processing and has strong applications in communication and information fields. This book summarizes and organizes the fundamental achievements of Fourier analysis theory research over the past 50 years, with strong systematicity, advanced, and comprehensive content. The author Loukas Grafakos, a native of Athens, Greece, obtained his Ph.D. from the University of California, Los Angeles, and is currently a professor of mathematics at the University of Missouri. He has been awarded the Kemper Fellow award for outstanding teaching and has co-authored or independently written 40 articles on Fourier analysis. The book covers Lp spaces and interpolation, maximal functions, Fourier transform, generalized functions, Fourier analysis on one-dimensional tori, convolution-type singular integrals, Littlewood-Paley theory and multipliers, smoothness and function spaces, BMO and Carleson measures, non-convolution-type singular integrals, weighted inequalities, boundedness and convergence of Fourier integrals. The presentation style is easy to understand, and it can be read with only undergraduate knowledge. Each chapter includes a summary of prerequisites, and there are abundant exercises and examples, making it an excellent textbook. At the end, a bibliography of 574 references is provided, which is also very useful for researchers.