ECU Libraries Catalog

Discrete analogues in harmonic analysis : Bourgain, Stein, and beyond / Ben Krause.

Author/creator Krause, Ben, 1988- author.
Format Book and Print
Publication Info Providence, Rhode Island : American Mathematical Society, [2022]
Copyright Notice ©2022
Descriptionxxvi, 563 pages : illustrations ; 26 cm.
Series Graduate studies in mathematics, 1065-7339 ; 224
Graduate studies in mathematics ; v. 224. ^A347883
Contents Part 1. Harmonic analytic preliminaries -- Tools -- On oscillation and convergence -- The linear theory -- Part 2. Discrete analogues in harmonic analysis : Radon transforms, I -- Bourgain's maximal functions on ℓ2(Z) -- Random pointwise ergodic theory -- An application to discrete Ramsey theory -- Bourgain's ℓ(Z)=argument, revisited -- Part 3. Discrete analogues in harmonic analysis: Radon transforms, II -- Ionescu-Wainger theory -- Establishing Ionescu-Wainger theory -- The spherical maximal function -- The lacunary spherical maximal function -- Part 4. Discrete improving inequalities -- Discrete analogues in harmonic analysis : Maximally modulated singular integrals -- Monomial "Carleson" operators -- Maximally modulated singular integrals : A theorem of Stein and Wainger -- Part 5. Discrete analogues in harmonic analysis : An introduction to multilinear theory -- Bilinear considerations -- Arithmetic Sobolev estimates: examples -- Part 6. Conclusion and appendices -- Further directions -- Remembering my collaboration with Stein and Bourgain-M. Mirek -- Appendix A. Introduction to additive combinatorics -- Appendix B. Oscillatory integrals and exponential sums.
Bibliography noteIncludes bibliographical references (pages 547-556) and index.
Issued in other formOnline version: Krause, Ben, 1988- Discrete analogues in harmonic analysis. Providence, Rhode Island : American Mathematical Society, [2022] 9781470471750
LCCN 2022024899
ISBN9781470468576 hardcover
ISBN1470468573 hardcover
ISBN9781470471743 paperback
ISBN1470471744 paperback
ISBNelectronic book

Available Items

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Joyner General Stacks QA403 .K64 2022 ✔ Available Place Hold