Lecture Course: Functional Analysis II

Tue, Thu 10 – 12   in B 041

Organisation of tutorials: Leo Wetzel

Problem sheets and further information

Synposis
This is a continuation of the lecture course Functional Analysis from the previous semester. Attendance of the latter is not a necessary prerequisite for this course. However, a background in the theory of Banach and Hilbert spaces will be required. Main topics to be covered are a proof of the spectral theorem for bounded self-adjoint operators, an introduction to unbounded symmetric and self-adjoint operators and the basics of the Fourier transform and distributions.

Prerequisites
Functional Analysis

Audience
Students pursuing the following degrees: MSc Mathematics, MSc Financial Mathematics, Elite Master Course Theoretical and Mathematical Physics

Literature
The course will not follow a particular textbook. The list below provides a short selection of English and German textbooks on general functional analysis and spectral theory (of which there are many!).

• M Reed and B Simon, Methods of modern Mathematical Physics I: Functional analysis, Academic Press, 1980
  [excellent textbook with a focus on spectral theory, not very gentle, proofs sometimes a bit brief; unfortunately rather pricey]
• D Werner, Funktionalanalysis, Springer, 2007
  [a German classic, covers a broad range of topics, including historical remarks]
• K Schmüdgen, Unbounded self-adjoint operators on Hilbert space, Springer, 2012
  [comprehensive and thorough treatment of unbounded operators, the spectral theorem and more advanced topics in spectral theory]
• M Dobrowolski, Angewandte Funktionalanalysis, Springer, 2006
  [the basics of functional analysis plus a thorough discussion of Sobolev spaces and elliptic PDE's]
• E Kreyszig, Introductory functional analysis with applications, Wiley, 1978
  [thorough and pedagogical, very explicit proofs, does not cover all topics treated in the course (e.g. no L^p-spaces)]
• P D Lax, Functional Analysis, Wiley, 2002
  [well readable with an emphasis on spectral theory and some applications to quantum mechanics]
• F Hirzebruch and W Scharlau, Einführung in die Funktionalanalysis, BI Mannheim, 1971
  [another German classic, elegant but very(!) concise]