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Notices of the American Mathematical Society Toronto Meetings (August 21- 26)- Page 413 Vl 0 0 Notices of the American Mathematical Society z s:: 3 0" ..,('tj >s:: August 1982, Issue 219 ()Q s:: Volume 29, Number 5, Pages 401-496 "'~ ..... Providence, Rhode Island USA \D 00 N ISSN 0002-9920 Calendar of AMS Meetings THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the Ameri· can Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and second announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meet­ ing. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the office of the Society in Providence. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for ab­ stracts submitted for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meeting announcement and the list of organizers of special sessions. MEETING ABSTRACT NUMBER DATE PLACE DEADLINE ISSUE 797 October 30-31, 1982 College Park, Maryland AUGUST 27, 1982 October 798 November 12-13, 1982 Baton Rouge, Louisiana AUGUST 24, 1982 October 7?9 November 12-13, 1982 East Lansing, Michigan SEPTEMBER 13, 1982 November 800 November 19-20, 1982 Monterey, California SEPTEMBER 20, 1982 November 801 January 5-9, 1983 Denver, Colorado OCTOBER 12, 1982 January (89th Arinuitl Meeting) 1983 March 18-19, 1983 Norman, Oklahoma April 14-15, 1983 New York, New York April 29-30, 1983 Salt Lake City, Utah August 8-12, 1983 Albany, New York (87th Summer Meeting) January 25-29, 1984 Louisville, Kentucky (90th Annual Meeting) January 9-13, 1985 Anaheim, California (91 st Annual Meeting) January 21-25, 1987 San Antonio, Texas (93rd Annual Meeting) DEADLINES: Advertising: (October Issue) September 9 (November Issue) September 30 News/Special Meetings: (October Issue) August 23 (November Issue) September 13 Other Events Sponsored by the Society August 21-22, 1982, AMS Short Course: Statistical Data Analysis, Toronto, Canada. This issue, page 414. April 12-13, 1983, AMS-SIAM Symposium on Inverse Problems, New York Statler Hotel, New York, New York. Subscribers' changes of addrass should be reported well in advance to avoid disruption of service: address labels are prepared four to six weeks in advance of the date of mailing. Requests for a change of address should always include the member or subscriber code and preferably a copy of the entire mailing label. Members are reminded that U. S. Postal Service change-of­ address forms are not adequate for this purpose, since they make no provision for several important items of information which are essential for the AMS records. Suitable forms are published from time to time in the Notices (e.g. June 1980, page 378). Send change of address notices to the Society at Post Office Box 6248, Providence, Rl 02940. [Notices is published eight times a year (January, February, April, June, August, October, November, December) by the American Mathematical Society at 201 Charles Street, Providence, Rl 02904. Second class postage paid at Providence, Rl and additional ma~ing offices. POSTMASTER: Send address change notices to Membership and Sales Department, American Mathematical Society, Post Office Box 6248, Providence, Rl 02940.] Publication here of the Society's street address, and the other information in brackets above, is a technical requirement of the U. S. Postal Service. The street address should never be used by correspondents, unless they plan to deliver their messages by hand. Members are strongly urged to notify the Society themselves of address changes (in the manner described above), since (as explained above) reliance on the postal service change-of-address forms is liable to cause delays in processing such requests in the AMS office. Notices of the American Mathematical Society Volume 29, Number 5, August 1982 EDITORIAL COMMITTEE Ralph P. Boas, Ed Dubinsky Richard J. Griego, Susan Montgomery Mary Ellen Rudin, Bertram Walsh Everett Pitcher (Chairman) MANAGING EDITOR 402 Para-Differential Operators-Another Step Forward Lincoln K. Durst for the Method of Fourier, R. S. Strichartz ASSOCIATE EDITORS 406 Queries Hans Samelson, Queries Ronald L. Graham, Special Articles 407 News and Announcements SUBSCRIPTION ORDERS Subscription for Vol. 29 (1982): 411 Letters to the Editor $36 list, $18 member. The subscription 412 Election Information price for members is included in the annual dues. Subscriptions and orders 413 Future Meetings of the Society for AMS publications should be Toronto, August 23-26, 413 addressed to the American Mathematical Society, P.O. Box 1571, Annex Station, College Park, October 30-37, 455 Providence, Rl 02901. All orders must Baton Rouge, November 12-13, 457 be prepaid. East Lansing, November 72-73, 459 ORDERS FOR AMS BOOKS AND Monterey, November 19-20, 460 INQUIRIES ABOUT SALES, SUBSCRIP· Call for Topics, 461 TIONS, AND DUES may be made by Invited Speakers, 463; Special Sessions, 463; calling Carol-Ann Blackwood at Information for Organizers of Special 800·556-7774 (toll free in U.S.) between 8:00a.m. and 4:15p.m. eastern time, Sessions, 464 Monday through Friday. See page 17. 466 New AMS Publications CHANGE OF ADDRESS. To avoid 469 Special Meetings interruption in service please send address changes four to six weeks in 472 AMS Reciprocity Agreements (Supplement) advance. It is essential to include the member code which appears on the 473 Miscellaneous address label with all correspondence Personal Items, 473; Deaths, 473; regarding subscriptions. Visiting Mathematicians (Supplement), 474; INFORMATION ABOUT ADVERTISING Backlog of Mathematics Research Journals, 476 in the Notices may be obtained from Virginia Biber at 401-272-9500. 478 AMS Reports and Communications Treasurer's Report, 478; Recent CORRESPONDENCE, including changes of address ~hould be sent to American Appointments, 479; Reports of Past Meetings: Mathematical Society, P.O. Box 6248, Bryn Mawr, 480; Madison, 481; Officers and Providence, Rl 02940. Committee Members of the Society, 483 Second class postage paid at 487 Advertisements Providence, Rl, and additional mailing offices. Copyright © 1982 by the Classified Advertising, 487; American Mathematical Society. ElMS Subscription Forms, 489, 490; Printed in the United States of America. AMS Policy on Recruitment Advertising, 491 Para-Differential Operators- Another Step Forward for the Method of Fourier by Robert 8. Strichartz The theory of partial differential equations where ap(x) = (8F f8up)(x, u(x), .. .). The linear (p.d.e.'s) is of central importance in both pure p.d.e. (**) depends on the particular solution and applied research. The theory of linear p.d.e. 's u of (* ). Bony was able to show that certain has now reached a mature stage of development. regularity properties of solutions of (*) are also Questions about existence, uniqueness, regularity possessed by u. Third, the method involves and propagation of singularities can be answered studying the Fourier transform of u, and so traces for large classes of equations, and we can often its ancestry directly back to Fourier's work on the match qualitative features of the solutions-such heat equation. Fourth, the proofs are relatively as local existence, smoothness, or having a well­ easy. The key ideas are conceptual rather than posed Cauchy problem-with formal properties computational, and the details of actually carrying of the equation. On the other hand, the theory out the proofs are not technically demanding. In of nonlinear p.d.e. 's is only beginning to emerge. this article I will explain the key ideas of the Since it is no secret that nature is usually method, but first I will review briefly the history nonlinear (in fact most of our favorite linear of Fourier's method in the recent past. equations, such as the wave equation, were derived A linear p.d.e. of order m can be written from oversimplified physical models in order to eliminate their nonlinearity) this is a welcome development. Of course much of the work being {1) Pu = ,L: aa(x{ ::z;) "'u(x) = f(x). done is very technical and specialized, and thus lal~m difficult for the nonexpert to appreciate; but there Substituting the Fourier inversion formula are aspects of the current work on nonlinear p.d.e.'s that are closely connected with other areas of mathematics and may serve to stimulate u(x) = {2!) ... I u.we•"'-ede developments far from their initial domain. In this article I will discuss one such development, where the theory of para-differential operators (para­ d.o.'s), which I believe should be of interest to the mathematical community (a survey of some and using the obvious relations rather different aspects of the theory of nonlinear p.d.e.'s, by L. Nirenberg has appeared [1]). Para-differential operators were very recently (:xr u(x) = (2!) ... 1u({)(i{)"'e'"'·ede introduced by Jean-Michel Bony [3] in order to prove some remarkable theorems about nonlinear leads to the equation partial differential equations. The results are remarkable for at least four reasons. First, they {2) (2!)"' I p(x, {)u({)e'"'·Ed{ = f(x) apply to the most general nonlinear p.d.e., (*) F(x, u(x), .
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