Funciones de una variable real con valores en un espacio vectorial de convergencia. I: derivadas.
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Autores: Fernando Castañeda Bravo
- Localización: Revista matemática hispanoamericana, ISSN 0373-0999, Vol. 42, Nº. 4-6, 1982, págs. 113-132
- Idioma: español
- Títulos paralelos:
- Functions of a real variable with values in a convergence vector space. I: derivatives
- Enlaces
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Resumen
Any order derivations of functions of a real variable with values in a convergence vector space over R (c.v.s.) have been defined. This will allow us to develop (in a following paper) the integration for this type of functions. Some results have been obtained: we build up a c.v.s. isomorphism between a c.v.s. F and the c.v.s. L(R;F) -the continuous linear mappings of R into F endowed with the continuous convergence structure Ac-. We prove a function f: R ? F to be of class Cn if, and only if, it is of class Cnc, n Î N. The relation among the derivative of any order of a function with values in a finite product of c.v.s. and the derivatives of the component functions has been established. A formula for the derivative of any order for the product of m functions, and another one for the higher derivative of a composed function are given. Some other results have been established.
