Seminars and courses of the Lab. The Zoom coordinates for the seminars delivered in Bologna are: https://unibo.zoom.us/j/86406355645?pwd=SzhUd3FIa3V1emZSVFZOK0svQ3I4dz09#success Passcode: 779096 Please verify if the seminar will be streamed on the seminar's page.
Seminars
Seminario II, Dipartimento di Matematica, Piazza di Porta San Donato 5, 40126, Bologna
We will present two classical results by Beurling and Lax characterizing invariant subspaces of the shift operator on the Hardy space of the unit disc and of the upper half plane, respectively.
Seminars
Aula Enriques, Dipartimento di Matematica, Piazza di Porta San Donato 5, 40126, Bologna
Why doing analysis on trees, besides the intrinsic interest? We show as application the characterization of the Carleson measures (or "trace measures") for the Dirichlet space. The seminar requires virtually no prerequisite on holomorphic functions.
Crash course
Seminario I, Dipartimento di Matematica, Piazza di Porta San Donato 5, 40126, Bologna
Interpolation sequences in general RKHS
Seminars
Seminario I, Dipartimento di Matematica, Piazza di Porta San Donato 5 40126, Bologna
On a metric space (X,d) one can define a set function called capacity. To any compact subset E of X can be associated a measure m on X, called equilibrium measure for E, such that m(E)=cap(E). We will give a characterization of equilibrium measures when X is a locally finite tree of infinite depth.
Seminars
Aula Bombelli, Dipartimento di Matematica, Piazza di Porta San Donato 5, 40126, Bologna
Interpolating sequences for the Nevanlinna class will be used to discuss a natural problem on finitely generated ideals in the class.
Seminars
Aula Bombelli, Dipartimento di Matematica, Piazza di Porta San Donato 5, 40126, Bologna
If H is a space of functions defined on some set X and the point evaluation functionals are bounded on H, we call the overall structure a Reproducing Kernel Hilbert Space (RKHS). We will lay down the basics of the theory as in the seminal article of Aronszajn and provide some examples.
Seminars
Seminario VIII, Dipartimento di Matematica, Piazza di Porta San Donato 5, 40126, Bologna
Following Arcozzi, Rochberg, Sawyer and Wick we give a (very brief) introduction to the potential theory on a polytree, and then present a very incomplete list of related problems.
Seminars
Seminario I, Dipartimento di Matematica, Piazza di Porta San Donato 5, 40126, Bologna
In 1983 Tom Wolff proved a surprising inequality which proved to be a pivotal tool in Nonlinear Potential Theory. I will go through Wolff's proof, but in the dyadic setting.