Integral Representations of Bounded Hankel Forms Defined in Scattering Systems with a Multiparametric Evolution Group
The notion of Hankel and Toeplitz forms acting in algebraic scattering systems is introduced. Particular examples of such systems are the classical scattering structures on Hilbert spaces as well as the trigonometric polynomials under the shift operator. In this last example, the Hankel and Toeplitz forms acting in it coincide with the usual ones. Given two positive Toeplitz forms in a scattering system, the Hankel forms bounded with respect to the hilbertian seminomas they define, have Toeplitz extensions similarly bounded, as well as Fourier representations. These results still hold when the discrete 1-parametric evolution group of the system is replaced by a continuous or a d-parametric one. Several applications to harmonic analysis are obtained.
KeywordsMatrix Measure Positive Form Fourier Representation Lift Property Scattering System
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