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Garrido, M. Isabel ; Jaramillo Aguado, Jesús Ángel ; Rangel, Yenny C. | Oxford University Press | 2009-12For an infinite-dimensional Riemannian manifold M we denote by C1b(M) the space of all real bounded functions of class C(1) on M with bounded derivative. In this paper we shall see how the natural structure of normed algebra on C1b(M) characteri[...]texto impreso
Biström, P. ; Jaramillo Aguado, Jesús Ángel ; Lindström, M. | Polish acad sciences inst mathematics | 1995This article deals with bounding sets in real Banach spaces E with respect to the functions in A(E), the algebra of real analytic functions on E, as well as to various subalgebras of A(E). These bounding sets are shown to be relatively weakly co[...]texto impreso
We study the existence of everywhere differentiable functions which are almost everywhere solutions of quite general Hamilton-Jacobi equations on open subsets of R(d) or on d-dimensional manifolds whenever d > = 2. In particular, when M is a Rie[...]texto impreso
We present an example showing that a classical result due to Glaeser about the closedness of composition subalgebras of infinitely differeuniable functions cannot be extended to the case of weakly uniformly differentiable functions on Banach spacestexto impreso
We introduce a suitable notion of asymptotic smoothness on infinite dimensional Banach spaces, and we prove that, under some structural restrictions on the space, the convex envelope of an asymptotically smooth function is asymptotically smooth.[...]texto impreso
We relate the moduli of asymptotic uniform smoothness and convexity of a Banach space with the existence of upper and lower l(p)-estimates of sequences in the space. To this end, we introduce two properties which are related to the (m(p))-proper[...]texto impreso
In this note we prove that the uniformity of a complete metric space X is characterized by the vector lattice structure of the set U(X) of all uniformly continuous real functions on X.texto impreso
Garrido, M. Isabel ; Jaramillo Aguado, Jesús Ángel ; Prieto Yerro, M. Ángeles | Real Academia de Ciencias Exactas, Físicas y Naturales | 2000This short article addresses natural problems such as this one: Let M and N be two Banach manifolds such that the algebras of real-analytic functions on M and N are isomorphic as algebras. Does it follow that M and N are real-analytic isom[...]texto impreso
It is shown that, in contrast to the complex case, every paracompact finite-dimensional real-analytic manifold can be embedded as a bounded and closed real-analytic submanifold of every infinite-dimensional real Banach space.texto impreso
In this article it is proved that any set in a real Banach space on which the C-infinity-functions are bounded, is relatively compact. In particular, for any real Banach space E, a sequence (x(n)) convergences to x in E if and only if f(x(n)) --[...]texto impreso
Azagra Rueda, Daniel ; Gómez Gil, Javier ; Fry, Robb ; Lovo, Mauricio ; Jaramillo Aguado, Jesús Ángel | Oxford University Press | 2005-03We show that if X is a Banach space having an unconditional basis and a Cp-smooth Lipschitz bump function, then for every C1-smooth function f from X into a Banach space Y, and for every continuous function ? : X ? (0, ?), there exists a Cp-smoo[...]texto impreso
Jaramillo Aguado, Jesús Ángel ; Jiménez Sevilla, María del Mar ; Sánchez González, L. | American Mathematical Society | 2014-03In this note we give sufficient conditions to ensure that the weak Finsler structure of a complete C-k Finsler manifold M is determined by the normed algebra C-b(k)(M) of all real-valued, bounded and C-k smooth functions with bounded derivative [...]texto impreso
The authors survey some recent results concerning the question when the equality HomA=E holds for a subalgebra A of the algebra C(E) of continuous real-valued functions on a real Banach space E. A new natural proof for this equality is given in [...]texto impreso
Jaramillo Aguado, Jesús Ángel ; Jiménez Sevilla, María del Mar ; Rodenas Pedregosa, J.L. ; Sánchez González, L. | Pergamon-Elsevier | 2015The concept of subdifferentiability is studied in the context of C-1 Finsler manifolds (modeled on a Banach space with a Lipschitz C-1 bump function). A class of Hamilton-Jacobi equations defined on C-1 Finsler manifolds is studied and several r[...]
