Noticias Destacadas
 Agenda del Departamento |
- Información (provisional) sobre grupos y horarios de las asignaturas impartidas por el Departamento de Matemáticas, para el curso 2023-2024.
- Propuestas de Trabajos de Fin de Grado para el curso 2023-2024.
|
Canal @matematicasuamEnlace al canal del Departamento en youtube. |
|
PIM (Pequeño Instituto de Matemáticas)Con el objetivo de fomentar el interés por las matemáticas y dirigido a jóvenes entre 14 y 18 años, nace este proyecto de Instituto de Ciencias Matemáticas (ICMAT) en colaboración con nuestro Departamento, la Universidad Autónoma de Madrid y la Real Sociedad Matemática Española. El proyecto comienzó en el curso académico 2022-2023. Ampliar información en su página web. |
|
|
|
|
|
|
|
|
|
|
| Anual | Mensual | Semanal | Hoy | Buscar | Ir al mes específico | ||||
|
|
|||||||||
Título: Aleksandrov-Clark measures and composition operators
Ponente: Pekka Nieminen (University of Helsinki, Finlandia)
Fecha/Hora: Miércoles, 16 de diciembre de 2015, a las 15:00 (2 horas)
Lugar: Aula 520, Módulo 17, Departamento de Matemáticas, Facultad de Ciencias, UAM
Resumen: Let ϕ be an analytic map taking the unit disc into itself. Then ϕ determines a family of positive measures τα supported on the unit circle and defined by the Poisson integral Re (α+ϕ(z)) / (α- ϕ(z)) = ∫ Pz dτα for every α on the unit circle. These measures were introduced by D.N. Clark (1972) in a spectral-theoretic context and many of their deep function-theoretic properties were later established by A.B. Aleksandrov (1987).
We start by examining basic function-theoretic properties of the family τα; in particular, the correspondence between the atoms of τα and the angular derivatives of ϕ. We also discuss Aleksandrov's disintegration formula for the Lebesgue measure.
The Aleksandrov-Clark measures induce a natural integral operator for functions defined on the unit circle. This operator, often called the Aleksandrov operator, has very nice properties as it preserves many important function spaces. It also turns out to have an intimate connection to the composition operator f → f ◦ ϕ induced by ϕ. This makes it possible to explain the operator-theoretic properties of composition operators in terms of the Aleksandrov-Clark measures.