حول الخطية الكسورية للمؤثر التركيبي على فضاء هاردي H2 == On Linear Fractional Composition Operator On Hardy Space H2
Author name:
عقيل محمد حسين
Supervisor name:
ايمان حسن عبود
General topic:
Mathematics
Specific topic:
Mathematics
Degree:
Master
University:
University of Kufa - College Of Education For Girls - Department Of Mathematics
Language:
English
University location:
Najaf
First pages:
27T350 - p.pdf
Abstract:
Let U denote the unit ball in the complex plane, the Hardy space H2 is the collection of functions Σ f (z) f ^ (n)zn holomorphic on U suchthat f ^ (n) with f (n) ^ denotes then the Taylor coefficient of f, where the norm is defined by ) n ( f f Σ The particular importance of H2 is due to the fact that it is a Hilbert space. Let φ be a holomorphic self - map of U, the composition operator Cφ induced by φ is defined on H2 by the equation C f = f φ (f ∈H2 ) φ o We have studied the composition operator induced by the special automorphism p α and discussed the adjoint of the composition of the symbol p α .We have look also at some known results on compositionoperators and tried to see the analogue results in order to show how the results are changed by changing the point p in U.In order to make the work accessible to the reader, we have included some known results with the details of the proofs for some cases and proofs for the results that once given in the literature with proofs.Finally, we hope that this will show that there is a lot of work that can be done in the area of composition operator.
