In the present paper we consider a class of entire functions represented by Dirichlet series whose coefficients belong to a commutative Banach algebra and prove it to be a complex FK-space and a Frechet space.
In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topo...In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topological vector spaces and it is in this context that we have chosen to present this work. We are interested in the topology of its spaces and in the topologies of their dual spaces. The first part, we presented the fundamental topological properties of topological vector spaces. The second part, we studied Frechet spaces and particularly the space S(R<sup>n</sup>) of functions of class C<sup>∞ </sup>on R<sup>n</sup> which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn</sup>) the space of tempered distributions. The last part aims to define a topological structure on an increasing union of Frechet spaces called inductive limit of Frechet spaces. We study in particular the space D(Ω) of functions of class C<sup>∞</sup> with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.展开更多
In this paper,we study the representation of linear operator on but abandom the Radon-Nikodym property and give a necessary and sufficient condition for representability of linear operator on by integral.
A recent nonlinear alternative for contraction maps in Frechet spaces due to Frigon and Granas （Resultats de type Leray-Schauder pour des contractions sur des espaces de Frechet, Ann. Sci. Math. Quebec 22, （2）, 161...A recent nonlinear alternative for contraction maps in Frechet spaces due to Frigon and Granas （Resultats de type Leray-Schauder pour des contractions sur des espaces de Frechet, Ann. Sci. Math. Quebec 22, （2）, 161-168 （1998））, combined with semigroup theory, is used to investigate the existence and uniqueness of mild solutions for first- and second-order functional semi linear and neutral damped differential equations in Frechet space.展开更多
In this paper, we use the concepts of (F, ρ) invexity, (F, ρ) quasiinvexity and (F,ρ) pseudoinvexity etc. to discuss the generalized convex programming min f(x) s.t. g i(x) 0 (i=1,…,m) g j(x)=0 ...In this paper, we use the concepts of (F, ρ) invexity, (F, ρ) quasiinvexity and (F,ρ) pseudoinvexity etc. to discuss the generalized convex programming min f(x) s.t. g i(x) 0 (i=1,…,m) g j(x)=0 (j=1,…, n), x ∈ Xand obtain various duality theorems. Where X is a Frechet space. f,g i(i=1,…, m) and h j(j=1, …, n) are functions from X to R 1.展开更多
文摘In the present paper we consider a class of entire functions represented by Dirichlet series whose coefficients belong to a commutative Banach algebra and prove it to be a complex FK-space and a Frechet space.
文摘In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topological vector spaces and it is in this context that we have chosen to present this work. We are interested in the topology of its spaces and in the topologies of their dual spaces. The first part, we presented the fundamental topological properties of topological vector spaces. The second part, we studied Frechet spaces and particularly the space S(R<sup>n</sup>) of functions of class C<sup>∞ </sup>on R<sup>n</sup> which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn</sup>) the space of tempered distributions. The last part aims to define a topological structure on an increasing union of Frechet spaces called inductive limit of Frechet spaces. We study in particular the space D(Ω) of functions of class C<sup>∞</sup> with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.
文摘In this paper,we study the representation of linear operator on but abandom the Radon-Nikodym property and give a necessary and sufficient condition for representability of linear operator on by integral.
文摘A recent nonlinear alternative for contraction maps in Frechet spaces due to Frigon and Granas （Resultats de type Leray-Schauder pour des contractions sur des espaces de Frechet, Ann. Sci. Math. Quebec 22, （2）, 161-168 （1998））, combined with semigroup theory, is used to investigate the existence and uniqueness of mild solutions for first- and second-order functional semi linear and neutral damped differential equations in Frechet space.
文摘In this paper, we use the concepts of (F, ρ) invexity, (F, ρ) quasiinvexity and (F,ρ) pseudoinvexity etc. to discuss the generalized convex programming min f(x) s.t. g i(x) 0 (i=1,…,m) g j(x)=0 (j=1,…, n), x ∈ Xand obtain various duality theorems. Where X is a Frechet space. f,g i(i=1,…, m) and h j(j=1, …, n) are functions from X to R 1.
