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We associate a family of Hilbert spaces H
q
2;(D) of analytic functions on the unit disk D=z
:|z|<1 the q-continuous Gegenbauer polynomials C
n
(x;q) on the interval]–1;1[ and give a q-analogue of the unitary integral transform that Watanabe constructed from the Hilbert space L
2(]–1;1[;(1–x
2)–
dx onto the weighted Hilbert space H
2;(D). 相似文献
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