Resumen: The authors are concerned with the characterization of those functions holomorphic on EC′ which are Fourier transforms of elements of ï¥â€² (E). Here E is a complete bornological vector space over R, ï¥ (E) stands for the space of all complex-valued C∞ -functions on E, and EC denotes the complexification and E′ the (bornological) dual of E.
The authors start with carrying over the classical Paley-Wiener-Schwartz theorem from RN to vector spaces E which have finite-dimensional bornology. (The only important infinite-dimensional member of this class seems to be ⊕NR, the space of finite sequences.) Then they show that the counterexample of S. Dineen and L. Nachbin [Israel J. Math. 13 (1972), 321–326 (1973)] extends to all vector spaces which possess an infinite-dimensional bounded set, i.e., the Paley-Wiener-Schwartz condition (PWS) does not give the desired characterization in most cases. Finally they formulate a further condition A and they prove that a function holomorphic on EC′ is the Fourier transform of an element of E′ (E) if and only if it satisfies PWS and A, provided E is endowed with a nuclear bornology. For Banach spaces E, a similar result was obtained by T. Abuabara earlier [Advances in holomorphy (Rio de Janeiro, 1977), pp. 1–29, North-Holland, Amsterdam, 1979].
Resumen: Se investiga la figura intelectual, profesional y personal de una de las primeras mujeres que accedió a un título de Economía en la Universidad de Cambridge, primera profesora adjunta a cátedra de Economía en esa universidad, que vivió en una época y lugar científicamente privilegiados dentro de la economía -Inglaterra en plena ebullición y desarrollo del análisis neoclásico-, en que se asentaron las bases para su consideración científica y por vez primera se
profesionalizó la Economía.
ABSTRACT: the figure of Mary Paley Marshall, the first woman who took the Moral Science Tripos (of which Political Economy formed a part) at Cambridge University and the first female lecturer in economics, to women students at first and mixed classes later. She lived during the period of the development of neoclassical analysis when economics was for the first time being considered as a science. She also made a major contribution to the professionalization of economics.
Palabras clave: Marshall, Mary Paley, Mujeres economístas, Inglaterra
Descriptores: space of homogeneous type; Triebel-Lizorkin space; localization principle; atom; Littlewood-Paley S-function; Calder´on-Zygmund reproducing formula
Resumen: The author establishes the localization principle for the Triebel-Lizorkin spaces on spaces of homogeneous type.
