When the Identity Theorem "
The Identity Theorem states that an analytic function (real or complex) on a connected domain is uniquely determined by its values on a sequence of distinct points that converge to a point of its domain. This result is not true in general in the real setting if we relax the analyticity hypothesis on...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/50443 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/50443 |
| Access Level: | acceso abierto |
| Palabra clave: | Lineability Spaceability Algebrability Analytic function Identity theorem Annulling function MATEMATICA APLICADA |
| Sumario: | The Identity Theorem states that an analytic function (real or complex) on a connected domain is uniquely determined by its values on a sequence of distinct points that converge to a point of its domain. This result is not true in general in the real setting if we relax the analyticity hypothesis on the function to infinitely many times differentiability. In fact, we construct an algebra of functions A enjoying the following properties: (i) A is uncountably infinitely generated (that is, the cardinality of a minimal system of generators of A is c), (ii) every nonzero element of A is nowhere analytic, (iii) A ⊂ C∞(R), (iv) every element of A has infinitely many zeroes in R, and (v) for every f ∈ A and n ∈ N, f (n) (the n-th derivative of f) enjoys the same properties as the elements in A\{0}. This construction complements those made by Cater and Kim & Kwon, and published in the American Mathematical Monthly in 1984 and 2000, respectively |
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