Programme Intensive Reminder (for Analysis on Manifolds)





Announcements:
  • The material for all subjects of the first two lectures can be found in the lecture notes [1],[2],[3] and in the books by S. Lang and F. Warner.



  • Spring semester 2013

     
  • Meeting 1: Wednesday, January 30, 10:00 - 13:00, location: 611 (Mathematics building, at UU)
  • Teacher: Marius Crainc
  • manifolds, smooth map
  • tangent vectors, vector fields
  • vector bundles.

  • Meeting 2: Wednesday, January 30, 14:00 - 17:00, location: 611 (Mathematics building, at UU)
  • Teacher: Marius Crainic
  • differential forms
  • partitions of unity
  • integration, densities

  • Meeting 3: Thursday, January 31, 10:00 - 13:00, location: 611 (Mathematics building, at UU)
  • Teacher: Erik van den Ban
  • Banach spaces, Hilbert spaces, locally convex vector spaces
  • examples: $L^2$, smooth functions (with supports), distributions.

  • Meeting 4: Thursday, January 31, 14:00 - 17:00, location: 611 (Mathematics building, at UU)
  • Teacher: Erik van den Ban
  • Schwartz spaces, the Fourier transform (Sobolev spaces?).
  • Compact operators, Fredholm operators.
  • Literature

    The following literature will be available in the mathematics library, just for consultance, not for take out.

  • Lang, Serge. Differential Manifolds. Addison-Wesley Publishing Company, 1972.
  • Warner, Frank W. Foundations of differentiable manifolds and Lie groups.
    Corrected reprint of the 1971 edition. Graduate Texts in Mathematics, 94. Springer-Verlag, New York-Berlin, 1983. ix+272 pp. ISBN: 0-387-90894-3
  • F. Treves, "Topological vector spaces, distributions and kernels", Academic Press, New York-London 1967 xvi+624 pp.
  • L. Schwarz, "Functional Analysis", Courant Institute of Mathematical Sciences, 1964
  • Ho"rmander, Lars. The analysis of linear partial differential operators. I. Distribution theory and Fourier analysis.
    Reprint of the second (1990) edition. Classics in Mathematics. Springer-Verlag, Berlin, 2003. x+440 pp. ISBN: 3-540-00662-1 35-02
  • Ho"rmander, Lars. Linear partial differential operators.
    Springer Verlag, Berlin-New York, 1976. vii+285 pp. 35-XX (46FXX)
  • Suggested lecture notes

  • [1] Prerequisites from differential geometry (E.P. van den Ban)
  • [2] Lie derivatives, tensors and forms (E.P. van den Ban)
  • [3]