Roman Bessonov University of Ljubljana "Schur's algorithm in inverse spectral theory"
I will discuss how to use the classical Schur's algorithm for analytic functions as a tool for solving inverse spectral problems. The connection between Schur's algorithm and Spectral theory was found very recently. Among other things, it gives sharp spectral stability results for Dirac operators with potentials of class L^2. I will discuss these results and formulate some open questions.
Kelly Bickel Bucknell University "Some Clark Theory on the Bidisk"
Classical Clark measures are singular measures on the unit circle defined via inner functions that are closely tied to important topics in operator theory and complex analysis (for example, model spaces, compressed shifts, and composition operators). In this talk, we’ll consider an analogous definition for Clark measures associated with two-variable inner functions. For certain classes of such functions, we’ll give exact formulas for these Clark measures, characterize when associated Clark embeddings are unitary, and obtain nice unitary perturbations of pairs of compressed shift operators.
This is joint work with John Anderson, Palak Arora, Linus Bergqvist, Joseph Cima, Conni Liaw, and Alan Sola.
James Brennan University of Kentucky "A Weighted Approximation Problem"
Karim Kellay Université de Bordeaux "Complete Interpolating Sequences for Fock Type Spaces"
We obtain a characterization of complete interpolating sequences in a class of Fock-type spaces with radial weights for which such sequences exist. Our criterion is formulated in terms of logarithmic separation and controlled perturbations of a reference sequence satisfying an Avdonin-type condition. This provides a geometric description of complete interpolating sequences and extends previous results of Borichev–Lyubarskii and Baranov–Belov–Borichev on Riesz bases of reproducing kernels in Fock-type spaces. It also yields explicit density criteria for sampling and interpolating sequences.
This is joint work with Y. Omari
Stefano Meda Università degli Studi di Milano-Bicocca "Uncentred Hardy–Littlewood maximal operators on half balls"
Sandra Pott Lund University "Laplace-Carleson Embeddings: Completing the picture"
Motivated by applications in the control theory of infinite-dimensional systems, several authors have investigated the boundedness of the Laplace transform $\mathcal{L}: L^p(0, \infty) \rightarrow L^q( \mathbb{C}_+, \mu)$ in terms of properties of the measure $\mu$, with the case $q=p=2$ being the classical Carleson Embedding Theorem. We will cover the case $p >2$, thus completing the picture to all $p,q$ with $1/p + 1/q \le 1$. In case $p >2$, the Laplace-Carleson Embedding Theorem can also be seen as an appropriate replacement of the Hausdorff-Young inequality.
This is joint work with Eskil Rydhe (Lund).