Axiomatization of the degree of Fitzpatrick, Pejsachowicz and Rabier
In this paper, we prove an analogue of the uniqueness theorems of Führer [15] and Amann and Weiss [1] to cover the degree of Fredholm operators of index zero constructed by Fitzpatrick, Pejsachowicz and Rabier [13], whose range of applicability is substantially wider than for the most classical degr...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2022 |
| Country: | España |
| Institution: | Universidad Complutense de Madrid (UCM) |
| Repository: | Docta Complutense |
| Language: | English |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/71279 |
| Online Access: | https://hdl.handle.net/20.500.14352/71279 |
| Access Level: | Open access |
| Keyword: | Degree for Fredholm maps Uniqueness Axiomatization Normalization generalized additivity Homotopy invariance Generalized algebraic multiplicity Parity Orientability Álgebra Lógica simbólica y matemática (Matemáticas) 1201 Álgebra 1102.14 Lógica Simbólica |
| Summary: | In this paper, we prove an analogue of the uniqueness theorems of Führer [15] and Amann and Weiss [1] to cover the degree of Fredholm operators of index zero constructed by Fitzpatrick, Pejsachowicz and Rabier [13], whose range of applicability is substantially wider than for the most classical degrees of Brouwer [5] and Leray–Schauder [22]. A crucial step towards the axiomatization of this degree is provided by the generalized algebraic multiplicity of Esquinas and López-Gómez [8, 9, 25], χ, and the axiomatization theorem of Mora-Corral [28, 32]. The latest result facilitates the axiomatization of the parity of Fitzpatrick and Pejsachowicz [12], σ(⋅,[a,b]), which provides the key step for establishing the uniqueness of the degree for Fredholm maps. |
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