The Detectable Subspace for the Friedrichs Model: Applications of Toeplitz Operators and the Riesz–Nevanlinna Factorisation Theorem

We discuss how much information on a Friedrichs model operator (a finite rank perturbation of the operator of multiplication by the independent variable) can be detected from ‘measurements on the boundary’. The framework of boundary triples is used to introduce the generalised Titchmarsh–Weyl M-function and the detectable subspaces which are associated with the part of the operator which is ‘accessible from boundary measurements’. In this paper, we choose functions arising as parameters in the Friedrichs model in certain Hardy classes. This allows us to determine the detectable subspace by using the canonical Riesz–Nevanlinna factorisation of the symbol of a related Toeplitz operator.

Composition Operators Mapping Logarithmic Bloch Functions into Hardy Space

Characterizing the hyperbolic Hardy classes, several g-functions of hyperbolic type are introduced. Using this, necessary and sufficient conditions on the inducing self-maps are established for the boundedness of the composition operators from logarithmic Bloch spaces into Hardy spaces.

Frame properties of a part of an exponential system with degenerate coefficients in Hardy classes

A part of an exponential system with degenerate coefficients is considered. The frame properties (completeness, minimality, basicity, atomic decomposition) of this system in Hardy classes are studied in the case where the coefficients may not satisfy the Muckenhoupt condition.

Hadamard Multipliers and Abel Dual of Hardy Spaces

The paper is devoted to the study of Hadamard multipliers of functions from the abstract Hardy classes generated by rearrangement invariant spaces. In particular the relation between the existence of such multiplier and the boundedness of the appropriate convolution operator on spaces of measurable functions is presented. As an application, the description of Hadamard multipliers intoH∞is given and the Abel type theorem for mentioned Hardy spaces is proved.