34678 - Functional Analysis 2

Academic Year 2017/2018

  • Docente: Antonio Bove
  • Credits: 6
  • SSD: MAT/05
  • Language: Italian
  • Moduli: Antonio Bove (Modulo 1) Davide Guidetti (Modulo 2)
  • Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
  • Campus: Bologna
  • Corso: Second cycle degree programme (LM) in Mathematics (cod. 8208)

Course contents

Normed spaces; Banach spaces; linear and continuous operators between normed spaces; Baire theorem and applications; Banach-Steinhaus theorem; open mapping theorem and applivations; closed graph theorem; Hahn-Banach theorem and applcations; weak topologies; reflexive Banach spaces; Hilbert spaces; orthogonal projections in Hilbert spaces; Riesz theorem ; Lax-Milgram theorem; compact and self-adjoint operators in Hilbert spaces.

Sobolev spaces; Sobolev embedding theorem; Riesz-Kolmogorov theorem; Rellich-Kondrakov theorem; variational method for the study of elliptic problems; expansions in eigenfunctions; applications to mixed parabolic and hyperbolic problems:

Semigroups and evolution equations; resolvent of a linear operator; Hille-Yosida theorem; applications to mixed parabolic and hyperbolic problems; analytic semigroups; applications to mixed hyperbolic problems.

Office hours

See the website of Antonio Bove

See the website of Davide Guidetti