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On Some Aspects Of The Differential Operator, Panakkal Jesu Mathew

Mathematics Theses

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, …