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Séminaire d'Analyse

Dual of de Branges spaces and Toeplitz operators

Carlo Bellavita

( Barcelona )

Salle 1

12 juin 2025 à 14:00

Inner functions are fundamental in complex analysis, but their impact on Toeplitz

operators acting in the Hardy space H1(C+)H^1(\mathbb{C}^+) presents intriguing questions:

Is the Toeplitz operator TΘT_{\overline\Theta}, with Θ{\overline\Theta} being the conjugate of an inner function,

bounded in H1(C+)H^1(\mathbb{C}^+)?

If not, what is the most natural space for its definition?

In this talk, we will explore these questions, revealing their connections to the duals

of 1-de Branges spaces.

This work stems from an ongoing collaboration with Marco Peloso.


References

[1] Bellavita C., Peloso M. On Toeplitz operators on H1(C+), Proc. Amer. Math. Soc..

[2] Bellavita C., Peloso M. Duality, BM O and Hankel operators on Bernstein spaces, J. Funct. Anal. 288-2 (2025).