Hilbert space 3C. For each element x in 3C the function | E(-)x\2 is a countably ... NIH-GM-13138-01 from the National Institute of General Medical Sciences. 610.
A TRANSFORMATION THEOREM ON SPECTRAL MEASURES1 HABIB SALEHI
1. Introduction. Let 03 be a 2-measurable/unction 0. smallest
let
positive
w(o)=oo.
integer
Define
For any point a in 12 let n(a) be the
such that
T"aEA;
if no such integer
Ak= [aEA\n(a)=k\,
= {aEA\n(a)=k}.
Borrowing
(l)
pn = »|r»u
the notation
A=Q —A,
exists
and
Tk
of [3] we will define
r„+1 yj ■ ■ ■},
for n\%\. We will also make use of the usual combinatorial
(k)j = k(k —1) • • • (k—j + l) for k and j positive (*)o = l.
symbol
integers,
with
Our object will be to prove that
J.A [n(a)Um
= j(j - 1) £
00 (k)u^pk+i
k=j-2
Received by the editors August 1, 1966. 1 Fellow of the John Simon Guggenheim
Memorial
Foundation.
Research
sup-
ported in part by the U. S. Air Force under Contract AF 18(600)-685 with Cornell University. 8 These moments
have also been obtained
by F. H. Simons, Notice
Eindhoven Technical School, December 23, 3966. License or copyright restrictions may apply to redistribution; see http://www.ams.org/journal-terms-of-use
