Semiadditive Functionals Research Articles

When is the space of semi-additive functionals an absolute (neighbourhood) retract?

In the present paper proved that if for a given compact Hausdorff space X the hyperspace exp(X) is a contractible compact space then the space OSf(X) is also a contractible compact space. As a consequence it is established that the space OSf(X) of semi-additive functionals is absolute (neighbourhood) retract if and only if the hyperspace exp(X) is so.

Dimension of Extremal Boundary of the Space of Semiadditive Functionals

In the paper, the extremal boundary of the space of weakly additive, order-preserving, normalized, positive-homogeneous, and semiadditive functionals on a compact space is studied. The dimension of the extremal boundary of the convex compact OS(n) is found.

Categorical and topological properties of the functor of Radon functionals

In this paper we introduce a functor OSR of semiadditive Radon functionals in the category Tych of Tychonoff spaces, which extends the functor OS:Comp→Comp of semiadditive functionals. It is proved that the functor OSR:Tych→Tych is normal in the category of Tychonoff spaces.

Semi-additive functionals of semi-Markov processes and measure-valued Poisson equation

In this paper, we consider a continuous-time semi-Markov process (SMP) in Polish spaces. We first introduce the semi-additive functional in semi-Markov cases, a natural generalization of the additive functional of Markov process (MP). The main contribution of this paper is the properties of semi-additive functional aforementioned. First, semi-additive functionals of SMPs are characterized in terms of a càdlàg function with zero initial value and a measurable function. Second, the necessary and sufficient conditions are investigated under which a semi-additive functional of SMP is a semimartingale, a local martingale, or a special semimartingale respectively. By the way, the Itô type formula is given. Finally, we study the expected cumulative discounted value of the semi-additive functional of an SMP. We prove that it solves a measure-valued Poisson equation and give the uniqueness conditions.

Modified Steklov Functions

We obtain estimates for nonnegative semiadditive functionals on the space of continuous 2π-periodic functions defined in terms of Steklov functions.

On the functor of semiadditive τ-smooth functionals

In the work we investigate categorical and topological properties of the functor OSτ of semiadditive τ-smooth functionals in the category Tych of Tychonoff spaces and their continuous mappings, which extends the functor OS of semiadditive functionals in the category Comp of compact spaces and their continuous mappings. It is proved that the functor OSτ is a normal functor in the category Tych of Tychonoff spaces.

Estimates of Semiadditive Functionals via Deviations of Steklov Functions in the Space L 2

We establish upper estimates for nonnegative semiadditive functionals defined on the space of periodic functions L 2 in terms of deviations of Steklov functions of even order in L 2.

Extreme boundary of the space semi-additive functionals on the four-point set

The present paper devoted to study of the extreme boundary of the convex compact set of all semi-additive functionals on the four-point compactum. We shall find some classes of extreme points of the space semi-additive functionals OS(4).

Countably Semiadditive Functionals and the Hardy-Littlewood Maximal Operator

Abstract: We describe the continuity of nonlinear Hardy–Littlewood maximal operator in nonmetricable function space , is a measurable subset of Rn with finite measure.

On geometric properties of functors of positive-homogenous and semiadditive functionals

We investigate the functor OH of positive-homogenous functionals and the functor OS of semiadditive functionals. We prove that OH(X) is an absolute retract if and only if X is an open-generated compactum, and OS(X) is an absolute retract if and only if X is an opengenerated compactum of weight ≤ ω 1 . We investigate the softness of mappings of multiplication of monads generated by these functors.

Semi-additive functionals and cocycles in the context of self-similarity

Kernel functions of stable, self-similar mixed moving averages are known to be related to nonsingular flows. We identify and examine here a new functional occuring in this relation and study its properties. To prove its existence, we develop a general result about semi-additive functionals related to cocycles. The functional we identify, is helpful when solving for the kernel function generated by a flow. Its presence also sheds light on the previous results on the subject.

Estimates for functionals by deviations of the Riesz sums in seminormed spaces

Suppose that (X, p) is a sermonized space, $ \left\{ {xk} \right\}_{k = 0}^n $ is a linearly independent system of elements in X, $ \left\{ {c_k } \right\}_{k = 0}^n $ is a sequence of linear bounded functionals such that c k (x l ) = δ kl , $$ R_{n,r} (x) = \sum\limits_{k = 0}^n {\left( {1 - \left( {\frac{k}{n + 1}} \right)^r } \right)ck(x)x_k } $$ are the Riesz sums. We prove general assertions concerning estimates from above for the values of semiadditive functionals $ \Phi :X \to \mathbb{R}_{ + } $ by deviations of the Riesz sums p(x − R n,r (x)). Bibliography: 6 titles.

The continuity of semiadditive functionals

In this paper we examine a general principle of continuity of semiadditive functionals on a metric linear space (MLS) that extends various results obtained previously in this respect. In particular, from our fundamental Theorem 1 it is easy to obtain Banach's closed graph theorem, the Banach-Steinhaus theorem, the weak base theorem, and others.

A theorem for semiadditive functionals

A theorem for semiadditive functionals