ABSTRACT
We associate a family of Hilbert spaces H q 2 ; λ ( D ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187834/69daaf7f-2564-4f2f-9a9d-3a9774ce28b0/content/eq1912.tif"/> of analytic functions on the unit disk D = {z ∈ C : |z| < 1} to the q-continuous Gegenbauer polynomials C n λ ( x ; q ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187834/69daaf7f-2564-4f2f-9a9d-3a9774ce28b0/content/eq1913.tif"/> on the interval ] – 1; 1[ as described in [5], and we give a q-analogue of the unitary integral transform of Watanabe [6] from the Hilbert space L 2 ( ] − 1 ; 1 [ ; ( 1 − x 2 ) λ − 1 2 d x ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187834/69daaf7f-2564-4f2f-9a9d-3a9774ce28b0/content/eq1914.tif"/> onto the weighted Hilbert space H 2;λ (D).
