Parametrization and Schur algorithm for the integral representation of Hankel forms in T-square
- Autores: Pedro Alegría Ezquerra
- Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 43, Fasc. 3, 1992, págs. 253-272
- Idioma: inglés
- Títulos paralelos:
- Parametrización y algoritmo de Schur para la representación integral de las formas de Hankel en T-cuadrado
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Resumen
The parametrization problem of the minimal unitary extensions of an isometric orperator allows its application, through the spectral theorem, to the case of the Fourier representations of a bounded Hankel form with respect to the norms $(\int\vert f\vert^2d\mu_1)^{1/2}$ and $(\int\vert f\vert^2d\mu_2)^{1/2}$ where $\mu_1,\mu_2\geq 0$ are finite measures in $\mathbb{T} \sim\vert0,2\pi)$. In this work we develop a similar procedure for the two-parametric case, where $\mu_1, \mu_2\geq 0$ are measures defined in $\mathbb{T}^2\sim\vert 0, 2\pi)\times\vert 0, 2\pi)$. With this purpose, we define the generalized Toeplitz forms on the space of two-variable trigonometric polynomials and use the lifting existence theorems of Cotlar and Sadosky. We provide a parametrization formula which is also valid in the special case of the Nehari problem and gives rise to a Schur-type algorithm for this problem.
