An Analytic Characterization of
p
,
q
-White Noise Functionals
Keyword(s):
In this paper, a characterization theorem for the S -transform of infinite dimensional distributions of noncommutative white noise corresponding to the p , q -deformed quantum oscillator algebra is investigated. We derive a unitary operator U between the noncommutative L 2 -space and the p , q -Fock space which serves to give the construction of a white noise Gel’fand triple. Next, a general characterization theorem is proven for the space of p , q -Gaussian white noise distributions in terms of new spaces of p , q -entire functions with certain growth rates determined by Young functions and a suitable p , q -exponential map.
2002 ◽
Vol 05
(03)
◽
pp. 395-407
◽
Keyword(s):
2017 ◽
Vol 20
(02)
◽
pp. 1750007
◽
1992 ◽
Vol 128
◽
pp. 65-93
◽
Keyword(s):
1991 ◽
Vol 123
◽
pp. 153-169
◽
Keyword(s):
1989 ◽
Vol 01
(02n03)
◽
pp. 313-323
◽