1
Banach Space
A normed linear space is a metric space w.r.t the metric d derived from its norm, where d(x, y) =
xy .
Denition A Banach space is a normed space that is a complete.
Example C(K) for K c
PDE and Functional Analysis
Winter term 2014/2015
Problem Sheet 13 (due Friday 23.01.2015)
University of Bonn
Prof. Dr. J. J. L. Velzquez
a
Dr. M. Helmers
Problem 1 (2+1 points)
1. Give an example of
PDE and Functional Analysis
University of Bonn
Winter term 2014/2015
Prof. Dr. J. J. L. Velzquez
a
Problem Sheet 14 (due Friday 30.01.2015 if you want it marked)
Dr. M. Helmers
Examination Information
PDE and Functional Analysis
Winter term 2014/2015
Problem Sheet 12 (due Friday 16.01.2015)
University of Bonn
Prof. Dr. J. J. L. Velzquez
a
Dr. M. Helmers
Important notes:
The nal problem sheet that
PDE and Functional Analysis
Winter term 2014/2015
Problem Sheet 11 (due Friday 09.01.2015)
University of Bonn
Prof. Dr. J. J. L. Velzquez
a
Dr. M. Helmers
Problem 1 (1+2+1 points)
1. Consider the oper
PDE and Functional Analysis
Winter term 2014/2015
Problem Sheet 9 (due Friday 12.12.2014)
University of Bonn
Prof. Dr. J. J. L. Velzquez
a
Dr. M. Helmers
Problem 1 (2+2 points)
Let X, Y, Z be real nor
PDE and Functional Analysis
Winter term 2014/2015
Problem Sheet 10 (due Friday 19.12.2014)
University of Bonn
Prof. Dr. J. J. L. Velzquez
a
Dr. M. Helmers
Problem 1 (1+2 points)
Let X be a Banach spac
PDE and Functional Analysis
Winter term 2014/2015
Problem Sheet 8 (due Friday 05.12.2014)
University of Bonn
Prof. Dr. J. J. L. Velzquez
a
Dr. M. Helmers
Problem 1 (3+1+1 points)
Let Rn be open and bo
PDE and Functional Analysis
Winter term 2014/2015
Problem Sheet 7 (due Friday 28.11.2014)
University of Bonn
Prof. Dr. J. J. L. Velzquez
a
Dr. M. Helmers
Problem 1 (3 points)
Let 0 < 1 and Rn be open
PDE and Functional Analysis
Winter term 2014/2015
Problem Sheet 5 (due Friday 14.11.2014)
University of Bonn
Prof. Dr. J. J. L. Velzquez
a
Dr. M. Helmers
Problem 1 (2+1+1 points)
Let Rn be open and u
PDE and Functional Analysis
Winter term 2014/2015
Problem Sheet 2 (due Friday 24.10.2014)
University of Bonn
Prof. Dr. J. J. L. Velzquez
a
Dr. M. Helmers
Problem 1 (Closed sets in metric spaces, 2+2 p
PDE and Functional Analysis
Winter term 2014/2015
Problem Sheet 6 (due Friday 21.11.2014)
University of Bonn
Prof. Dr. J. J. L. Velzquez
a
Dr. M. Helmers
Problem 1 (4 points)
Let
1
1/2
M=
u C 0 ([0, 1
PDE and Functional Analysis
Winter term 2014/2015
Problem Sheet 4 (due Friday 07.11.2014)
University of Bonn
Prof. Dr. J. J. L. Velzquez
a
Dr. M. Helmers
Problem 1 (An interpolation inequality, 2 poin
PDE and Functional Analysis
Winter term 2014/2015
Problem Sheet 3 (due Friday 31.10.2014)
University of Bonn
Prof. Dr. J. J. L. Velzquez
a
Dr. M. Helmers
Problem 1 (Convergence in Hilbert spaces, 1+1
PDE and Functional Analysis
Winter term 2014/2015
Problem Sheet 1 (due Friday 17.10.2014)
University of Bonn
Prof. Dr. J. J. L. Velzquez
a
Dr. M. Helmers
Problem 1 (Either-Or Topology, 2 points)
Let X
Difference equations are now used in all areas of science: in biology, demography,
ecology, economics, engineering, finance, and physics.
This course is an introduction to discrete dynamical systems.