Orthogonally additive holomorphic functions of bounded type over C(K)

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 o...

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Autores principales:	Carando, D., Lassalle, S., Zalduendo, I.
Formato:	JOUR
Materias:	holomorphic functions over C(K) integral representation orthogonally additive
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00130915_v53_n3_p609_Carando
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_00130915_v53_n3_p609_Carando
record_format	dspace
spelling	todo:paper_00130915_v53_n3_p609_Carando2023-10-03T14:10:40Z Orthogonally additive holomorphic functions of bounded type over C(K) Carando, D. Lassalle, S. Zalduendo, I. holomorphic functions over C(K) integral representation orthogonally additive 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. Fil:Carando, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Lassalle, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Zalduendo, I. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00130915_v53_n3_p609_Carando
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	holomorphic functions over C(K) integral representation orthogonally additive
spellingShingle	holomorphic functions over C(K) integral representation orthogonally additive Carando, D. Lassalle, S. Zalduendo, I. Orthogonally additive holomorphic functions of bounded type over C(K)
topic_facet	holomorphic functions over C(K) integral representation orthogonally additive
description	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.
format	JOUR
author	Carando, D. Lassalle, S. Zalduendo, I.
author_facet	Carando, D. Lassalle, S. Zalduendo, I.
author_sort	Carando, D.
title	Orthogonally additive holomorphic functions of bounded type over C(K)
title_short	Orthogonally additive holomorphic functions of bounded type over C(K)
title_full	Orthogonally additive holomorphic functions of bounded type over C(K)
title_fullStr	Orthogonally additive holomorphic functions of bounded type over C(K)
title_full_unstemmed	Orthogonally additive holomorphic functions of bounded type over C(K)
title_sort	orthogonally additive holomorphic functions of bounded type over c(k)
url	http://hdl.handle.net/20.500.12110/paper_00130915_v53_n3_p609_Carando
work_keys_str_mv	AT carandod orthogonallyadditiveholomorphicfunctionsofboundedtypeoverck AT lassalles orthogonallyadditiveholomorphicfunctionsofboundedtypeoverck AT zalduendoi orthogonallyadditiveholomorphicfunctionsofboundedtypeoverck
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Orthogonally additive holomorphic functions of bounded type over C(K)

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