- Title
- On a class of pseudo-differential operators in IRⁿ
- Creator
- Matjila, D M
- Subject
- Pseudodifferential operators Operator theory
- Date Issued
- 1988
- Date
- 1988
- Type
- Thesis
- Type
- Masters
- Type
- MSc
- Identifier
- vital:5392
- Identifier
- http://hdl.handle.net/10962/d1001981
- Description
- The class of pseudo-differential operators with symbols from Sm (superscript) po̧̧ (subscipt)(Ωx IRⁿ) has been extensively studied.The main assumption which characterises this class of symbols is that a(x,Ȩ) є Sm (superscript)po̧̧ (subscipt)(Ωx IRⁿ) should have a polynomial growth in the Ȩ variable only. The x-variable is controlled on compact subsets of Ω. A polynomial growth in both the x and Ȩ variables on a C°°(lR²ⁿ) function a(x,Ȩ) gives rise to a different class of symbols and a corresponding class of operators. In this work, such symbols and the action of the operators on the functional spaces S(lRⁿ) , S'(lRⁿ) and the Sobolev spaces Qs (superscript) (lRⁿ) (s є lRⁿ) are studied. A study of the calculus (i.e. transposes, adjoints and compositions) and the functional analysis of these operators is done with special attention to L-boundedness and compactness. The class of hypoelliptic pseudo-differential operators in IRⁿ is introduced as a subclass of those considered earlier.These operators possess the property that they allow a pseudo- inverse or parametrix. In conclusion. the spectral theory of these operators is considered. Since a general spectral theory would be beyond the scope of this work, only some special cases of the pseudo-differential operators in IRⁿ are considered. A few applications of this spectral theory are discussed
- Format
- 109 leaves
- Format
- Publisher
- Rhodes University
- Publisher
- Faculty of Science, Mathematics
- Language
- English
- Rights
- Matjila, D.M
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RU Department of Mathematics (Pure and Applied)
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