Unitary parts of generalized Hankel operators

Generalized Unitary Operators

1. Let C be the complex field and T be the unit circle { \ £ C : | \ | = 1} . For a non-negative integer m or for m = oo, let OCT) be the space of all m-times continuously differentiable functions on T. (Here we consider T as a C°°-manifold in the natural way. Thus, any / £ C m ( r ) can be identified with an m-times continuously differentiable periodic function f (6) of a real variable 0 with ...

Distorted Hankel Integral Operators

For α, β > 0 and for a locally integrable function (or, more generally , a distribution) ϕ on (0, ∞), we study integral ooperators G α,β ϕ on L 2 (R +) defined by G α,β ϕ f (x) = R+ ϕ x α + y β f (y)dy. We describe the bounded and compact operators G α,β ϕ and operators G α,β ϕ of Schatten–von Neumann class S p. We also study continuity properties of the averaging projection Q α,β onto the oper...

Slant Hankel Operators

Eigenstructure of nonlinear Hankel operators

This paper investigates the eigenstructure of Hankel operators for nonlinear systems. It is proved that the variational system and Hamiltonian extension can be interpreted as the Gâteaux differentiation of dynamical input-output systems and their adjoints respectively. We utilize this differentiation in order to clarify the eigenstructure of the Hankel operator, which is closely related to the ...

Wiener-hopf plus Hankel Operators on the Real Line with Unitary and Sectorial Symbols

Wiener-Hopf plus Hankel operators acting between Lebesgue spaces on the real line are studied in view of their invertibility, one sided-invertibility, Fredholm property, and the so-called n and d–normal properties. This is done in two different cases: (i) when the Fourier symbols of the operators are unitary functions, and (ii) when the Fourier symbols are related with sectorial elements appear...