DP00BD62 Introduction to function spaces (5 cr)
Cooperation network course
Network: Cross-institutional studies in advanced courses in mathematics and statistics
This course is offered through the Network for Advanced Studies in Mathematics. These studies are available for the following degree students:
- Bachelor's Degree Programme in Mathematics
- Master's Degree Programme in Mathematics
- Bachelor's Degree Programme in Mathematics (Subject Teacher)
- Master's Degree Programme in Mathematics (Subject Teacher)
- Bachelor's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Master's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Doctoral Programme in Mathematics and Statistics
- Doctoral Programme in Mathematics and Science (Specialication in Mathematics)
Description
Lebesgue spaces, Schwartz spaces, Fourier transform, tempered distributions, Sobolev spaces
Learning outcomes
Upon completion of the course, the student will be able to:
• Define Lebesgue spaces and describe their basic properties.
• Compute the Fourier transform of functions in the Schwartz space.
• Perform basic operations on tempered distributions, including differentiation and Fourier transform.
• Define and calculate weak derivatives, and construct Sobolev spaces of integer and fractional order.
• Apply Sobolev embedding theorems to analyze smoothness and regularity of functions.
Additional information
Course is aimed to students in mathematical sciences (applied and computational mathematics).
Description of prerequisites
Complex analysis 1, Calculus 2, Measure theory