Artículo
Carando, D.; Lassalle, S.; Zalduendo, I. "Orthogonally additive holomorphic functions of bounded type over C(K)" (2010) Proceedings of the Edinburgh Mathematical Society. 53(3):609-618
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Abstract:
It is known that all k-homogeneous orthogonally additive polynomials P over C(K) are of the form P(x)= ∫Kxkdμ. Thus, x → xk factors all orthogonally additive polynomials through some linear form μ. We show that no such linearization is possible without homogeneity. However, we also show that every orthogonally additive holomorphic function of bounded type f over C(K) is of the form f(x)=∫Kh(x)dμ for some μ and holomorphic h : C (K) → L1(μ) of bounded type. Copyright © Edinburgh Mathematical Society 2010.
Registro:
| Documento: | Artículo |
| Título: | Orthogonally additive holomorphic functions of bounded type over C(K) |
| Autor: | Carando, D.; Lassalle, S.; Zalduendo, I. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina Departamento de Matemática, Universidad Torcuato di Tella, Miñones 2177, C1428ATG, Buenos Aires, Argentina |
| Palabras clave: | holomorphic functions over C(K); integral representation; orthogonally additive |
| Año: | 2010 |
| Volumen: | 53 |
| Número: | 3 |
| Página de inicio: | 609 |
| Página de fin: | 618 |
| DOI: | http://dx.doi.org/10.1017/S0013091509000248 |
| Título revista: | Proceedings of the Edinburgh Mathematical Society |
| Título revista abreviado: | Proc. Edinburgh Math. Soc. |
| ISSN: | 00130915 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00130915_v53_n3_p609_Carando |
Referencias:
- Aron, R., Berner, P., A Hahn-Banach extension theorem for analytic mappings (1978) Bull. Soc. Math. France, 106 (1), pp. 3-24
- Benyamini, Y., Lassalle, S., Llavona, J.G., Homogeneous orthogonally additive polynomials on Banach lattices (2006) Bull. Lond. Math. Soc., 38 (3), pp. 459-469
- Carando, D., Lassalle, S., Zalduendo, I., Orthogonally additive polynomials over C(K) are measures: A short proof (2006) Integ. Eqns Operat. Theory, 56, pp. 597-602
- Davie, A., Gamelin, T., A theorem on polynomial-star approximation (1989) Proc. Am. Math. Soc., 106 (2), pp. 351-356
- Dimant, V., Galindo, P., Maestre, M., Zalduendo, I., Integral holomorphic functions (2004) Studia Math., 160, pp. 83-99
- Dineen, S., Holomorphic functions on a Banach space (1970) Bull. Am. Math. Soc., 76, pp. 883-886
- Dineen, S., (1999) Complex Analysis on Infinite Dimensional Spaces, , Springer
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Citas:
---------- APA ----------
Carando, D., Lassalle, S. & Zalduendo, I. (2010) . Orthogonally additive holomorphic functions of bounded type over C(K). Proceedings of the Edinburgh Mathematical Society, 53(3), 609-618.http://dx.doi.org/10.1017/S0013091509000248
---------- CHICAGO ----------
Carando, D., Lassalle, S., Zalduendo, I. "Orthogonally additive holomorphic functions of bounded type over C(K)" . Proceedings of the Edinburgh Mathematical Society 53, no. 3 (2010) : 609-618.http://dx.doi.org/10.1017/S0013091509000248
---------- MLA ----------
Carando, D., Lassalle, S., Zalduendo, I. "Orthogonally additive holomorphic functions of bounded type over C(K)" . Proceedings of the Edinburgh Mathematical Society, vol. 53, no. 3, 2010, pp. 609-618.http://dx.doi.org/10.1017/S0013091509000248
---------- VANCOUVER ----------
Carando, D., Lassalle, S., Zalduendo, I. Orthogonally additive holomorphic functions of bounded type over C(K). Proc. Edinburgh Math. Soc. 2010;53(3):609-618.http://dx.doi.org/10.1017/S0013091509000248
