Functional Analysis A.A. 2024-2025

Schema della sezione

• Seleziona sezione Presentation of the course 2025-2026

  Minimizza Espandi

  Presentation of the course 2025-2026

  Minimizza tutto Espandi tutto

  Preliminary program:
  

  1. Measure theory and integration.
  2. Spaces of random variables with finite p-moment.
  3. Elements of Fourier Analysis.

  
  Bibliography:
  

  • Lecture notes by the teacher
  • A. Bressan Lecture~notes in Functional Analysis with application to linear partial differential equations . AMS 2012.
  • G. B. Folland Real Analysis: modern tecniques and their applications. Wiley 1999 (2nd ed)
  • F. Santambrogio Optimal transport for applied mathematicians Birkhauser/Springer Cham 2015. 

     

  
  Schedule for November-December 2025: 
  • tuesday November 4 10-13
  • tuesday November 18 10-13.30
  • thursday November 20 10-13
  • thursday November 27 10-13
  • tuesday December 2 10-13.30
  • wednesday December 10 10-13
  • tuesday December 16  10-13
  
  Final exam (written exam): January 13, 2026, Ugge' room, time 10-12 (duration of the exam 90m minutes).

  • Seleziona attività Lecture notes

    

    Lecture notes File
  • Seleziona attività Annunci

    

    Annunci Forum
• Seleziona sezione Course record

  Minimizza Espandi

  Course record

  • Seleziona attività November 4: characterization of sigma-finite Borel measures on R

    

    November 4: characterization of sigma-finite Borel measures on R File
  • Seleziona attività November 18: measurable functions, push forward of a measure, integration w.r.t a measure, Radon Nikodym theorem

    

    November 18: measurable functions, push forward of a measure, integration w.r.t a measure, Radon Nikodym theorem File
  • Seleziona attività November 20: absolutely continuous measure and singular measures. Joint law of two random variables. Metric spaces and Banach spaces.

    

    November 20: absolutely continuous measure and singular measures. Joint law of two random variables. Metric spaces and Banach spaces. File
  • Seleziona attività November 27: Jensen inequality, Holder inequality. Banach spaces of rando variables with finite p-moment. Scalar product in M^2.

    

    November 27: Jensen inequality, Holder inequality. Banach spaces of rando variables with finite p-moment. Scalar product in M^2. File
  • Seleziona attività November 27 registration

    

    November 27 registration Kaltura Video Resource
• Seleziona sezione Past exams

  Minimizza Espandi

  Past exams

  • Seleziona attività Exam January 2025, with sketch of solutions

    

    Exam January 2025, with sketch of solutions File
  • Seleziona attività Exam December 2023 with sketch of solutions

    

    Exam December 2023 with sketch of solutions File
  • Seleziona attività Exam December 2022, with sketch of solutions

    

    Exam December 2022, with sketch of solutions File
  • Seleziona attività Exam December 2021, with sketch of solutions

    

    Exam December 2021, with sketch of solutions File