Resumen de Two-parametric liftings of Toeplitz forms
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~[0,2p[ (see [1]). In this work we develop a similar procedure for the two-parametric case, where µ1, µ2 are positive measures defined in T2~[0,2p[x[0,2p[. 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.
