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MULTIPLIERS AND A PALEY-WIENER THEOREM FOR REAL REDUCTIVE GROUPS
 

Summary: 1
MULTIPLIERS AND A PALEY-WIENER THEOREM
FOR REAL REDUCTIVE GROUPS
James Arthur
The classical Paley-Wiener theorem is a description of the image
of Cc(OR) under Fourier transform. The Fourier transform
f(A) = f(x)eAX dx
-00
is defined a priori for purely imaginary numbers A, but if f has
compact support f will extend to an entire function on the complex
plane. The image of C((R) under this map is the space of entirec
functions F with the following property - there exists a constant
N such that
supflF(A) e-NIRe Al(1 + lIm A)n] <
AeC
for every integer n. (There is a similar theorem which characterizes
the image of the space of compactly supported distributions.)
Our purpose is to describe an analogous result for a reductive
Lie group. We shall also discuss a closely related theorem on
multipliers, a result whose statement is especially simple. Both

  

Source: Arthur, James G. - Department of Mathematics, University of Toronto

 

Collections: Mathematics