Description of the structure of singular spectrum for Friedrichs model operator near singular point
The study of the point spectrum and the singular continuous one is reduced to investigating the structure of the real roots set of an analytic function with positive imaginary part M(λ). We prove a uniqueness theorem for such a class of analytic functions. Combining this theorem with a lemma on smoo...
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201011668 |
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| _version_ | 1832568390749782016 |
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| author | Serguei I. Iakovlev |
| author_facet | Serguei I. Iakovlev |
| author_sort | Serguei I. Iakovlev |
| collection | DOAJ |
| description | The study of the point spectrum and the singular continuous one is reduced to investigating the structure of the real roots set of an analytic function with positive imaginary part M(λ). We prove a uniqueness theorem for such a class of analytic functions.
Combining this theorem with a lemma on smoothness of M(λ) near its real roots permits us to describe the density of the singular
spectrum. |
| format | Article |
| id | doaj-art-de038ccfdf684cfeaf348f92d510407f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-de038ccfdf684cfeaf348f92d510407f2025-02-03T00:59:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-01281254010.1155/S0161171201011668Description of the structure of singular spectrum for Friedrichs model operator near singular pointSerguei I. Iakovlev0Departamento de Matematicas, Universidad Simon Bolivar, Apartado Postal 89000, Caracas 1080-A, VenezuelaThe study of the point spectrum and the singular continuous one is reduced to investigating the structure of the real roots set of an analytic function with positive imaginary part M(λ). We prove a uniqueness theorem for such a class of analytic functions. Combining this theorem with a lemma on smoothness of M(λ) near its real roots permits us to describe the density of the singular spectrum.http://dx.doi.org/10.1155/S0161171201011668 |
| spellingShingle | Serguei I. Iakovlev Description of the structure of singular spectrum for Friedrichs model operator near singular point International Journal of Mathematics and Mathematical Sciences |
| title | Description of the structure of singular spectrum for Friedrichs model operator near singular point |
| title_full | Description of the structure of singular spectrum for Friedrichs model operator near singular point |
| title_fullStr | Description of the structure of singular spectrum for Friedrichs model operator near singular point |
| title_full_unstemmed | Description of the structure of singular spectrum for Friedrichs model operator near singular point |
| title_short | Description of the structure of singular spectrum for Friedrichs model operator near singular point |
| title_sort | description of the structure of singular spectrum for friedrichs model operator near singular point |
| url | http://dx.doi.org/10.1155/S0161171201011668 |
| work_keys_str_mv | AT sergueiiiakovlev descriptionofthestructureofsingularspectrumforfriedrichsmodeloperatornearsingularpoint |