Some topics in the history of harmonic analysis in the twentieth century

G. B. Folland ()
Additional contact information
G. B. Folland: University of Washington

Indian Journal of Pure and Applied Mathematics, 2017, vol. 48, issue 1, 1-58

Abstract: Abstract In December 2015 I gave a series of six lectures at the Indian Institute of Science in which I sketched the thematic development of some of the main techniques and results of 20th-century harmonic analysis. The subjects of the lectures were, briefly, as follows: 1. Fourier series, 1900-1950. 2. Singular integrals (part I). 3. H p , BMO, and singular integrals (part II). 4. Littlewood-Paley theory: the history of a technique. 5. Harmonic analysis on groups. 6. Wavelets. I emphasized interconnections, both the way in which the material in the first lecture provided the roots out of which most of the developments in the other lectures grew, and the ways in which those developments interacted with each other. I included sketches of as many proofs as the time would permit: some very brief, but some fairly complete, especially those whose methodology is an important part of the subject. Much was omitted, of course, and there was a natural bias toward the areas where I have spent periods of my own mathematical life. Many developments, particularly those of the final quarter-century, received at most a brief mention. This paper is a written account of these lectures with a few more details fleshed out, a few topics reorganized, and a few items added. I hope that others may find it an interesting narrative and a useful reference, and that it may lead some of them to share my enjoyment of exploring the original sources. I have tried to provide the references to those sources wherever possible, and for the more recent developments I also provide references to various expository works as the occasion arises. For the pre-1950 results discussed here and their proofs, however, there is one canonical reference, which I give here once and for all: Antoni Zygmund’s treatise [96]. (The more fundamental ones can also be found in Folland [29].)

Keywords: Fourier analysis; harmonic analysis; singular integral operators; Hardy spaces; Littlewood-Paley theory; wavelets (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-016-0198-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:48:y:2017:i:1:d:10.1007_s13226-016-0198-z

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-016-0198-z

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().