TY  - BOOK
AU  - Krause,Ben
TI  - Discrete analogues in harmonic analysis: bourgain, stein, and beyond
T2  - Graduate studies in mathematics,
SN  - 9781470471743
U1  - 517.57 
PY  - 2022///
CY  - Rhode Island
PB  - American Mathematical Society
KW  - Harmonic analysis
KW  - Number theory
KW  - Dynamical systems and ergodic theory
KW  - Harmonic analysis on Euclidean spaces
N1  - Includes bibliographical references and index
N2  - This timely book explores certain modern topics and connections at the interface of harmonic analysis, ergodic theory, number theory, and additive combinatorics. The main ideas were pioneered by Bourgain and Stein, motivated by questions involving averages over polynomial sequences, but the subject has grown significantly over the last 30 years, through the work of many researchers, and has steadily become one of the most dynamic areas of modern harmonic analysis. The author has succeeded admirably in choosing and presenting a large number of ideas in a mostly self-contained and exciting monograph that reflects his interesting personal perspective and expertise into these topics. ―Alexandru Ionescu, Princeton University Discrete harmonic analysis is a rapidly developing field of mathematics that fuses together classical Fourier analysis, probability theory, ergodic theory, analytic number theory, and additive combinatorics in new and interesting ways. While one can find good treatments of each of these individual ingredients from other sources, to my knowledge this is the first text that treats the subject of discrete harmonic analysis holistically. The presentation is highly accessible and suitable for students with an introductory graduate knowledge of analysis, with many of the basic techniques explained first in simple contexts and with informal intuitions before being applied to more complicated problems; it will be a useful resource for practitioners in this field of all levels. ―Terence Tao, University of California, Los Angeles
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