Axiornatizing the algebraic multiplicity
Given a smooth family pound of one (real or complex) variable and taking values within the class of Fredholm operators of index zero in a Banach space, there are some available definitions of algebraic multiplicity of the family pound at a point lambda(0) of the parameter at which the operator ( p...
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| Format: | Conference item |
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2004
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| _version_ | 1797074899288719360 |
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| author | Mora-Corral, C |
| author_facet | Mora-Corral, C |
| author_sort | Mora-Corral, C |
| collection | OXFORD |
| description | Given a smooth family pound of one (real or complex) variable and taking values within the class of Fredholm operators of index zero in a Banach space, there are some available definitions of algebraic multiplicity of the family pound at a point lambda(0) of the parameter at which the operator ( pound lambda(0)) becomes non-invertible. This paper shows that the algebraic multiplicity is uniquely determined by a few of its properties, independently of its construction. The results which allowed R. J. Magnus(1) to prove the existence of the multiplicity are employed here to show the uniqueness. Also, some explicit formulae of the multiplicity are proved. |
| first_indexed | 2024-03-06T23:42:55Z |
| format | Conference item |
| id | oxford-uuid:6feb25b6-90b2-410a-b977-0f865a9da0fe |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:42:55Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:6feb25b6-90b2-410a-b977-0f865a9da0fe2022-03-26T19:33:51ZAxiornatizing the algebraic multiplicityConference itemhttp://purl.org/coar/resource_type/c_5794uuid:6feb25b6-90b2-410a-b977-0f865a9da0feSymplectic Elements at Oxford2004Mora-Corral, CGiven a smooth family pound of one (real or complex) variable and taking values within the class of Fredholm operators of index zero in a Banach space, there are some available definitions of algebraic multiplicity of the family pound at a point lambda(0) of the parameter at which the operator ( pound lambda(0)) becomes non-invertible. This paper shows that the algebraic multiplicity is uniquely determined by a few of its properties, independently of its construction. The results which allowed R. J. Magnus(1) to prove the existence of the multiplicity are employed here to show the uniqueness. Also, some explicit formulae of the multiplicity are proved. |
| spellingShingle | Mora-Corral, C Axiornatizing the algebraic multiplicity |
| title | Axiornatizing the algebraic multiplicity |
| title_full | Axiornatizing the algebraic multiplicity |
| title_fullStr | Axiornatizing the algebraic multiplicity |
| title_full_unstemmed | Axiornatizing the algebraic multiplicity |
| title_short | Axiornatizing the algebraic multiplicity |
| title_sort | axiornatizing the algebraic multiplicity |
| work_keys_str_mv | AT moracorralc axiornatizingthealgebraicmultiplicity |