# Two-parametric liftings of Toeplitz forms.

Extracta Mathematicae (1992)

- Volume: 7, Issue: 1, page 16-19
- ISSN: 0213-8743

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topAlegría 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 -

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