[General information] [Lecture notes] [Extra]

Contents

T1. LINEAR SPACES, METRIC SPACES, NORMED SPACES AND BANACH SPACES.


T2. SPACES WITH SCALAR PRODUCT. HILBERT SPACES.


T3. SPACES OF FUNCTIONS.


T4. LINEAR FORMS AND DUAL SPACE. THEORY OF DISTRIBUTIONS.


T5. OPERATORS IN HILBERT SPACES.


T6. SPECTRAL THEORY IN HILBERT SPACES.

Exercises

#1. Linear, metric and normed spaces.

#2. Pre-Hilbert and Hilbert spaces.

#3. Spaces of functions.

#4. Linear forms and theory of distributions.

#5. Operators.




Literature

[1] L. Abellanas, A. Galindo: Espacios de Hilbert, Eudema, 1987.
[2] A. Vera, P. Alegría: Un curso de Análisis Funcional. Teoría y problemas, AVL, 1997.
[3] G. Helmberg: Introduction to spectral theory in Hilbert space, Dover, 1997.
[4] P. Roman: Some modern mathematics for physicists and other outsiders, vol. 2. Pergamon, 1975.
[5] P. Lax: Functional Analysis, Wiley, 2002.
[6] A. Galindo, P. Pascual: Mecánica Cuántica, Eudema, 1989.
[7] E. Romera et al.: Métodos Matemáticos: problemas en espacios de Hilbert, operadores lineales y espectros, Paraninfo, 2013.