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Sameripour, Ali
- Topics on the Degenerate Elliptic Differential Operators far From Self Adjoint Ones
Authors
1 Department of Mathematics, Lorestan University, Khorramabad, Iran
Source
Indian Journal of Science and Technology, Vol 9, No 7 (2016), Pagination:Abstract
Background: Elliptic differential operators and asymptotic distribution of eigenvalues of them are discussed in many works.Methods: In this paper we get some new results about an important differential operator on a Hilbert space. Also asymptotic distribution of eigenvalues of this kind of differential operators are proved with new methods that estimation of the resolvent of the operators is used in this paper.Finding: We get some new theorems about the differential operator A. We consider a bounded domain with smooth boundary in define a norm and find the asymptotic distribution of eigenvalues of the operator in the space .Improvement: we improve the method of proving this kind of theorems.
Keywords
Asymptotic Distribution, Eigenvalues, Non-SelfAdjoint Elliptic Differential Operator, ResolventFull Text
- Spectral Properties of Differential Operators Constructed of Sectorial Forms
Authors
1 Department of Mathematics, Lorestan University, Khorramabad, Iran
Source
Indian Journal of Science and Technology, Vol 9, No 7 (2016), Pagination:Abstract
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 PropertiesFull Text