On Reproducing Kernel Hilbert Spaces of Polynomials
Copyright policy )On Reproducing Kernel Hilbert Spaces of Polynomials
AbstractCertain Hilbert spaces of polynomials, called Szegö spaces [11], are studied. A transformation, called Hilbert traneformation, is constructed for every polynomial associatted with a Szegö space. An orthogonal set is found in a Szegö space which determines the norm of the space. A matrix factorization theory is obtained for defining polynomials. Measures associated with a Szegö space are parametrized by functions which ue analytic and bounded by one in the unit disk. A fundmental factorization theorem relates Szegö spaces to weighted Hardy spaces.
- The University of Texas at Austin United States
norm determining orthogonal sets, Hilbert space of polynomials, Spaces of bounded analytic functions of one complex variable, reproducing kernel function, Special integral transforms (Legendre, Hilbert, etc.), Nevanlinna parametrization, Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces), generalized Hilbert transforms, matrix factorization theorems, Szegö space
norm determining orthogonal sets, Hilbert space of polynomials, Spaces of bounded analytic functions of one complex variable, reproducing kernel function, Special integral transforms (Legendre, Hilbert, etc.), Nevanlinna parametrization, Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces), generalized Hilbert transforms, matrix factorization theorems, Szegö space
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