L?rebok
Eidelman, Yuli; Milman, Vitali; Tsolomitis, Antonis: Functional analysis. An introduction, 2004. American Mathematical Society, Providence, RI. ISBN:?0-8218-3646-3.
Pensum
Pensum vil bli tatt fra de syv f?rste kapitlene i l?reboken. Se den detaljerte framdriftsplanen for detaljer. (We plan to cover most of the material in chapters 1-7, cf. the detailed teaching plan.)
Endelig pensum til eksamen/Final curriculum requirements for the exam: chapter 1, chapter 2 (excluding 2.3d), chapter 3, chapter 4, chapter 5, chapter 6 (excluding 6.2.11, 6.2.12, 6.4.8-6.4.10), chapter 7 (excluding 7.4), exercises.
Anbefalt tilleggslesning/Suggestions for additional reading
Peter D. Lax: Functional Analysis, 2002. Wiley. ISBN:?0-471-55604-1.
Boka til Lax dekker hele pensum i kursene MAT4340 og MAT4350, men g?r mye lenger i anvendelser. Grunnen til at den ikke brukes som l?rebok i kurset er at den inneholder for mye stoff. Den anbefales som tilleggslesning for alle som ?nsker ? g? videre i emner basert p? matematisk analyse.
Lax's book covers the curriculum requirements for the courses MAT4340 and MAT4350, and goes deeper into applications. However, it contains a lot more material than required for these courses. Nevertheless, it is recommended as additional reading for all those who wish to study further topics in analysis.
John Conway, An introduction to Functional Analysis, Springer-Verlag. (This book is a very pedestrian introduction to Functional Analysis, and can supply the material in the book by Eidelman et.al. both with regard to exercises but also to examples.)
Gert K. Pedersen, Analysis Now, Springer-Verlag. (This book covers material on topology, normed spaces and duality, Hilbert spaces and operators between these, and much more, including a chapter on measure and integration.)