Relatively bounded and compact perturbations of nth order differential operators
A perturbation theory for nth order differential operators is developed. For certain classes of operators L, necessary and sufficient conditions are obtained for a perturbing operator B to be relatively bounded or relatively compact with respect to L. These perturbation conditions involve explicit i...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171298000064 |
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| _version_ | 1832558758152110080 |
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| author | Terry G. Anderson |
| author_facet | Terry G. Anderson |
| author_sort | Terry G. Anderson |
| collection | DOAJ |
| description | A perturbation theory for nth order differential operators is developed. For certain
classes of operators L, necessary and sufficient conditions are obtained for a perturbing operator B to
be relatively bounded or relatively compact with respect to L. These perturbation conditions involve
explicit integral averages of the coefficients of B. The proofs involve interpolation inequalities. |
| format | Article |
| id | doaj-art-d9b3087e35db4a299f7162be67fd8634 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d9b3087e35db4a299f7162be67fd86342025-02-03T01:31:38ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251998-01-01211476810.1155/S0161171298000064Relatively bounded and compact perturbations of nth order differential operatorsTerry G. Anderson0Department of Mathematical Sciences, Appalachian State University, Boone 28608, NC, USAA perturbation theory for nth order differential operators is developed. For certain classes of operators L, necessary and sufficient conditions are obtained for a perturbing operator B to be relatively bounded or relatively compact with respect to L. These perturbation conditions involve explicit integral averages of the coefficients of B. The proofs involve interpolation inequalities.http://dx.doi.org/10.1155/S0161171298000064Perturbation theorydifferential operatorsrelatively bounded relatively compactintegral averagesinterpolation inequalitiesmaximal and minimal operators essential spectrumFredholm index. |
| spellingShingle | Terry G. Anderson Relatively bounded and compact perturbations of nth order differential operators International Journal of Mathematics and Mathematical Sciences Perturbation theory differential operators relatively bounded relatively compact integral averages interpolation inequalities maximal and minimal operators essential spectrum Fredholm index. |
| title | Relatively bounded and compact perturbations of
nth order differential operators |
| title_full | Relatively bounded and compact perturbations of
nth order differential operators |
| title_fullStr | Relatively bounded and compact perturbations of
nth order differential operators |
| title_full_unstemmed | Relatively bounded and compact perturbations of
nth order differential operators |
| title_short | Relatively bounded and compact perturbations of
nth order differential operators |
| title_sort | relatively bounded and compact perturbations of nth order differential operators |
| topic | Perturbation theory differential operators relatively bounded relatively compact integral averages interpolation inequalities maximal and minimal operators essential spectrum Fredholm index. |
| url | http://dx.doi.org/10.1155/S0161171298000064 |
| work_keys_str_mv | AT terryganderson relativelyboundedandcompactperturbationsofnthorderdifferentialoperators |