#### Date of Award

7-28-2006

#### Degree Type

Thesis

#### Degree Name

Master of Science (MS)

#### Department

Mathematics and Statistics

#### First Advisor

Dr. Lifeng Ding - Chair

#### Abstract

The Differential Operator D is a linear operator from C1[0,1] onto C[0,1]. Its domain C1[0,1] is thoroughly studied as a meager subspace of C[0,1]. This is analogous to the status of the set of all rational numbers Q in the set of the real numbers R. On the polynomial vector space Pn the Differential Operator D is a nilpotent operator. Using the invariant subspace and reducing subspace technique an appropriate basis for the underlying vector space can be found so that the nilpotent operator admits its Jordan Canonical form. The study of D on Pn is completely carried out. Finally, the solution space V of the nth order differential equation with leading coefficient one is studied. The behavior of D on V is explored using some notions from linear algebra and linear operators. NOTE- Due to the limitation of the above being in "text only form" , further details of this abstract can be viewed in the pdf file.

#### Recommended Citation

Mathew, Panakkal Jesu, "On Some Aspects of the Differential Operator." Thesis, Georgia State University, 2006.

https://scholarworks.gsu.edu/math_theses/12