Toeplitz operators on Dirichlet-Besov spaces

We study Toeplitz operators on the Besov spaces in the case of the open unit disk. We prove that a symbol satisfying a weak Lipschitz type condition induces a bounded Toeplitz operator. Such symbols do not need to be bounded functions or have continuous extensions to the boundary of the open unit disk. We discuss the problem of the existence of nontrivial compact Toeplitz operators, and also consider Fredholm properties and prove an index formula.

Schatten class Toeplitz operators on generalized Fock spaces

In this paper we characterize the Schatten p class membership of Toeplitz operators with positive measure symbols acting on generalized Fock spaces for the full range p>0.

Formal linguistic approaches to heritage language acquisition: bridges for pedagogically oriented research

The goal of this chapter is to lay out the central themes of heritage language acquisition research adopting a formal/theoretical linguistic perspective.  Specifically, we aim to provide a detailed discussion of the nature of heritage language grammars. In doing so, we will address the debates on how to explain heritage speaker competence differences from monolingual baselines and more. This chapter will not be limited to discussions of Spanish as a heritage language, but rather will highlight the important role that Spanish has played and will continue to play in the development of heritage language acquisition studies. Finally, we will offer some comments/insights on how the information covered regarding the formal linguistic properties of heritage speaker knowledge should be considered for and implemented in heritage language pedagogies and thus dealing with heritage speakers in the classroom setting.