arXiv subjects

Eugenio Alberto Dellepiane

Publications and source records attributed to Eugenio Alberto Dellepiane.

2 recordsLinked to original sources

arXiv2024

The spectral analysis of the difference quotient operator on model spaces

We conduct a spectral analysis of the difference quotient operator $Q^u_ζ$, associated with a boundary point $ζ\in \partial \mathbb{D}$, on the model space $K_u$. We describe the operator's spectrum and provide both upper and lower estimates for its norm, and furthermore discussing the sharpness of these bounds. Notably, the upper estimate offers a new characterization of the one-component property for inner function.

math.FA↗

arXiv2023

Embedding model and de Branges-Rovnyak spaces in Dirichlet spaces

In this paper we study embeddings between de Branges-Rovnyak spaces $H(b)$ and harmonically weighted Dirichlet spaces $\mathcal{D}(μ)$ in terms of the boundary spectrum of $b$ and the support of the measure $μ$, by using elementary reproducing kernel estimates. We completely characterize the embedding between the model spaces $K_u$ and the local Dirichlet spaces $\mathcal{D}_ζ$, and we discuss some applications.

math.FA↗