Sharpening the EDGE of the wedge theorem


Leon Ehrenpreis

Temple University


Harvard University

Thursday, May 6, 2004

Talk at 4:30 p.m. in Science Center D

Tea at 4:00 p.m. in the Math Lounge


Abstract:   Denote by O+ and O­ the positive and negative orthants in Rn. The wedges W+ and W­ are the tubes over O+ and O­. The edge is the intersection of the wedges, which is the imaginary space. Let f+ and f­ be functions which are holomorphic on W+ and W­. If f+ = f­ on the edge then there is a function F which is holomorphic on all of Cn which extends f+ and f­.

We shall sharpen and extend this result in several directions:

  1. Holomorphicity is defined by the Cauchy Riemann operator (d bar) which we shall replace by a general class of differential operators P(D).
  2. Problems in the spirit of Bill Clinton: What is "is" (for us "is" means =)?
    1. What is the weakest sense in which f+ = f­ on the edge? (Problem of Norman Levinson)
    2. (Problem of Fefferman-Nirenberg-Paul Yang) Instead of Pf ± = 0 we require only that Pf ± vanish rapidly at the edge.
    3. (quasianalyticity problem) Instead of Pf ± = 0 we give bounds on the Pmf±.

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Posted: April 28, 2004    URL: