Analogues of finite Blaschke products as inner functions
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We give a generalization of the notion of finite Blaschke products from the perspective of generalized inner functions in various reproducing kernel Hilbert spaces. Further, we study precisely how these functions relate to the so-called Shapiro--Shields functions and shift-invariant subspaces generated by polynomials. Applying our results, we show that the only entire inner functions on weighted Hardy spaces over the unit disk are multiples of monomials, extending recent work of Cobos and Seco.
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- University of Mary United States
- University of Toledo United States
- University System of Ohio United States
Bergman spaces and Fock spaces, Hardy spaces, Mathematics - Complex Variables, shift-invariant subspaces, Blaschke products, Functional Analysis (math.FA), Mathematics - Functional Analysis, FOS: Mathematics, reproducing kernel spaces, Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces), Complex Variables (math.CV), Spaces and algebras of analytic functions of one complex variable
Bergman spaces and Fock spaces, Hardy spaces, Mathematics - Complex Variables, shift-invariant subspaces, Blaschke products, Functional Analysis (math.FA), Mathematics - Functional Analysis, FOS: Mathematics, reproducing kernel spaces, Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces), Complex Variables (math.CV), Spaces and algebras of analytic functions of one complex variable
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