Two-parametric liftings of Toeplitz forms.

Alegría Ezquerra, Pedro. "Two-parametric liftings of Toeplitz forms.." Extracta Mathematicae 7.1 (1992): 16-19. <http://eudml.org/doc/39956>.

@article{AlegríaEzquerra1992,
abstract = {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.},
author = {Alegría Ezquerra, Pedro},
journal = {Extracta Mathematicae},
keywords = {Formas de Toeplitz; Operadores isométricos; Extensión; Parametrización; Polinomios trigonométricos},
language = {eng},
number = {1},
pages = {16-19},
title = {Two-parametric liftings of Toeplitz forms.},
url = {http://eudml.org/doc/39956},
volume = {7},
year = {1992},
}

TY - JOUR
AU - Alegría Ezquerra, Pedro
TI - Two-parametric liftings of Toeplitz forms.
JO - Extracta Mathematicae
PY - 1992
VL - 7
IS - 1
SP - 16
EP - 19
AB - 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.
LA - eng
KW - Formas de Toeplitz; Operadores isométricos; Extensión; Parametrización; Polinomios trigonométricos
UR - http://eudml.org/doc/39956
ER -