Distorted Hankel integral operators

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 ...

Hankel Multipliers and Transplantation Operators

Connections between Hankel transforms of different order for L-functions are examined. Well known are the results of Guy [Guy] and Schindler [Sch]. Further relations result from projection formulae for Bessel functions of different order. Consequences for Hankel multipliers are exhibited and implications for radial Fourier multipliers on Euclidean spaces of different dimensions indicated.

Hankel Operators on Hilbert Space

commonly known as Hilbert's matrix, determines a bounded linear operator on the Hilbert space of square summable complex sequences. Infinite matrices which possess a similar form to H, namely those that are 'one way infinite' and have identical entries in cross diagonals, are called Hankel matrices, and when these matrices determine bounded operators we have Hankel operators, the subject of thi...