Indian Journal of Science and Technology

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Background: Spectral properties and asymptotic distribution of eigenvalues of differential operators has been an important subject in mathematics and physics because they reflect many properties of the operators, moreover we can calculate some equalities and inequalities about differential operators. Methods: In this paper the main concepts and the basics of sectorial forms and m-sectorial operators are discussed in detail. Then we introduce a sectorial form that has an integral form and conclude some properties about it. Finally some spectral properties of differential operators constructed of this proposed sectorial form are studied. Finding: It is usual to prove spectral properties of differential operators by investigating resolvent estimates but in this paper we prove an important spectral theorem by using properties of bilinear forms instead of resolvent estimates. Improvement: We improve the method of proving the spectral theorems by using sectorial forms and getting a useful theorem about spectral properties of differential operators.


Keywords

Asymptotic Distribution, Eigenvalues, m-Sectorial Operators, Sectorial Forms, Spectral Properties
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