Type of Document Master's Thesis Author Mathew, Panakkal Jesu Author's Email Address pmathew2@student.gsu.edu URN etd-05182006-170911 Title On Some Aspects of the Differential Operator Degree Master of Science Department Mathematics and Statistics Advisory Committee
Advisor Name Title Dr. Lifeng Ding Committee Chair Keywords
- DIFFERENTIAL OPERATOR
- JORDAN CANONICAL FORM
- NILPOTENT OPERATORS
- LINEAR OPERATOR
Date of Defense 2005-05-11 Availability unrestricted 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 ofC[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.
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