13:15 Opening

13:20 Alan Sola

Pairs of Clark unitary operators on the bidisk and their Taylor joint spectrum

In the last couple of years, Clark measures associated with classes of inner functions 𝜙 have been characterized in several multivariate settings, including on the bidisk. In my talk, I will present recent progress on the operator theory side and explain how compressed shifts on two-variable model spaces can be perturbed to pairs of unitary operators. The perturbations involved are often infinite-dimensional, but under additional assumptions they admit fairly concrete descriptions. The Taylor joint spectrum for the resulting unitary operators is in turn identified with the support of Clark measures which take a particularly attractive form for rational inner functions.

This reports on joint work with Palak Arora, Kelly Bickel, and Constanze Liaw.

14:20 Break

14:30 Odysseas Bakas

Structural properties of the Hardy–Orlicz space H ^log and a dyadic approach to the study of products of functions in H ¹ and BMO

It was shown by A. Bonami, T. Iwaniec, P. Jones, and M. Zinsmeister that the product of a function in the Hardy space H ¹(𝔻) and a function in BMOA(𝔻) belongs to the Hardy-Orlicz space H ^log(𝔻), and that every function in H ^log(𝔻) can be written as such a product.

In the first part of the talk, we present results on certain structural properties of the Hardy-Orlicz space H ^log(𝔻). In the second part, we discuss dyadic counterparts of some of the results from the first part and outline a dyadic approach to the study of products of functions in H ¹ and BMO.

The talk is based on joint work with Sandra Pott, Salvador Rodríguez-López, and Alan Sola.

15:30 Break

15:50 Eskil Rydhe

Calderón--Hankel operators on the bidisk

Analogous to Calderón commutators, a Calderón--Hankel operator refers to a Hankel operator composed with differentiation. In the context of scalar-valued functions of one variable, Hankels and Calderón--Hankels share many qualities. In the context of vector-valued functions, some of these qualities persist for Calderón--Hankels but not for Hankels. The context of the bidisk constitutes a natural middle ground between the scalar- and vector-valued settings. In my talk, I will review some results for Calderón--Hankel operators in the one variable setting, and extend these to the bidisk setting. 

16:50 Closing