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Resumen de Two-parametric liftings of Toeplitz forms

Pedro Alegría Ezquerra Árbol académico

  • 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.


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