The parametrization problem of the minimal unitary extensions of an isometric operator allows its application, through the spectral theorem, to the case of the Fourier representations of a bounded Hankel form with respect to the norms (∫ |f|2dμ1)1/2 and (∫ |f|2dμ2)1/2 where μ1, μ2 are positive finite measures in T~[0,2π[ (see [1]). In this work we develop a similar procedure for the two-parametric case, where μ1, μ2 are positive measures defined in T2~[0,2π[x[0,2π[. With this purpose, we define the generalized Toeplitz forms on the space of the two-variable trigonometric polynomials and use the lifting existence theorems due to Cotlar and Sadosky [3]. We provide a parametrization formula which is also valid to the special case of the Nehari problem.
@article{urn:eudml:doc:39956,
title = {Two-parametric liftings of Toeplitz forms.},
journal = {Extracta Mathematicae},
volume = {7},
year = {1992},
pages = {16-19},
mrnumber = {MR1203434},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39956}
}
Alegría Ezquerra, Pedro. Two-parametric liftings of Toeplitz forms.. Extracta Mathematicae, Tome 7 (1992) pp. 16-19. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39956/