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Infinite dimensional Analysis
- Oggetto:
Infinite dimensional Analysis
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Academic year 2015/2016
- Teaching staff
- Prof. Alessandro PORTALURI (Lecturer)
Prof. Enrico Priola (Lecturer) - Type
- A scelta dello studente
- Credits/Recognition
- 6
- Course disciplinary sector (SSD)
- MAT/05 - analisi matematica
- Delivery
- Tradizionale
- Language
- Italiano
- Type of examination
- Orale
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Sommario del corso
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Program
• Short introduction to measure theory; Gaussian measures and their properties.
• First properties of infinite dimensional Gaussian measures in Banach and Hilbert spaces; Fernique Theorem, reproducing kernel and Cameron–Martin space.
• Zero–one laws and characterisation of the elements of the reproducing kernel.
• The space of Brownian motion and the characterisation of the reproducing kernel and of the Cameron–Martin space in the classical Wiener space.
• Integration by parts formulae, gradient and divergence, Sobolev functions on abstract Wiener spaces; definitions and basic properties.
• Short introduction to the semigroup theory; definition of the Ornstein– Uhlenbeck semigroup and operator and characterisation of its domain. Hermite polynomials, the Wiener Chaos Decomposition.
• Poincare' and Log-Sobolev inequalities and spectral properties of the Ornstein– Uhlenbeck operator.
Suggested readings and bibliography
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Il corso fa riferimento alle lezioni del 19th Internet Seminar: Infinite Dimensional Analysis:
http://dmi.unife.it/it/ricerca-dmi/seminari/isem19
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