Functional analysis

Teschl G.

Table of contents :
Preface……Page 6
0.1. Linear partial differential equations……Page 8
1.1. The Banach space of continuous functions……Page 12
1.2. The geometry of Hilbert spaces……Page 16
1.3. Completeness……Page 20
1.4. Bounded operators……Page 21
2.1. Orthonormal bases……Page 24
2.2. The projection theorem and the Riesz lemma……Page 28
2.3. Orthogonal sums and tensor products……Page 30
2.4. Compact operators……Page 31
2.5. The spectral theorem for compact symmetric operators……Page 33
2.6. Applications to Sturm-Liouville operators……Page 35
Bibliography……Page 38
Glossary of notations……Page 40
Index……Page 42