Sumários

Lecture 12

25 Outubro 2023, 11:00 Maria Teresa Faria da Paz Pereira

Complements of the Theorem of Spectral Decomposition for compact self-adjoint operators.


Lecture 11

23 Outubro 2023, 10:30 Maria Teresa Faria da Paz Pereira

Point spectrum of compact self-adjoint operators: main properties. Theorem of spectral decomposition of a compact self-adjoint operator.



TP 5

18 Outubro 2023, 11:30 Maria Teresa Faria da Paz Pereira

Examples and resolution of exercises of Chapter I.


Lecture 10

18 Outubro 2023, 11:00 Maria Teresa Faria da Paz Pereira

Ascoli-Arzelà Theorem: statement without a proof. The Fredholm integral operators are compact in C([a,b]) with the norm of uniform convergence. The Fredholm integral operators are compact in L^2([a,b]): main ideas for a proof.
Point spectrum for an operator T in L(E), E a normed space.


Lecture 9

16 Outubro 2023, 10:30 Maria Teresa Faria da Paz Pereira

Properties of adjoint and self-adjoint operators (cont.).
Compact linear operators between two normed spaces E,F: definitions and general properties. The space of compact linear operators is closed in L(E,F) if F is Banach. Examples of compact linear operators.