ANALISI IPERCOMPLESSA E GEOMETRIA
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- Versione italiana
- Academic year
- 2022/2023
- Teacher
- CINZIA BISI
- Credits
- 6
- Didactic period
- Secondo Semestre
- SSD
- MAT/03
Training objectives
- This is an advanced course in hypercomplex analysis and geometry taught in English : starting from the complex analysis and geometry , we generalize the principal results and concepts therein to the skew field of quaternions, when the lack of commutativity will permit it.
The course permits also to enter in a prosperous field of research nowadays , hence the students are encouraged to ask me Laurea Magistrale Thesis or Ph.D. Thesis . Prerequisites
- A first course in Complex Analysis
Course programme
- Definitions and basic algebraic results over the skew field H ( 4 hours )
Fundamental Theorem of Algebra : from C towards H (4 hours)
Def. of Slice Regularity and previous definitions in the literature (4 hours )
Fractional linear transformations on the unit ball of H ( 4 hours )
Regular power series (4 hours)
Zeros (5 hours)
Singularities ( 5 hours )
Integral Representations ( 4 hours )
Maximum Modulus and applications ( 4 hours )
Spherical series and differential ( 4 hours ) Didactic methods
- Lectures at the blackboard . Solving the home exercises with the help of students.
Learning assessment procedures
- One hour seminar at the blackboard on a chosen argument by the student , with questions all over the course. Exercises at the blackboard during the lectures.
Reference texts
- 1) A. Sudbery “Quaternionic Analysis” Math. Proc. Cambridge Philos. Soc. 85 (1979) 199-225.
2) G. Gentili, C. Stoppato, D. C. Struppa “Regular functions of a quaternionic variable” Springer Monographs in Mathematics , 2013. pp. 185.
3) H.D. Ebbinghauss et al.
“Numbers” GTM Springer 123.
