Search results for " space"
showing 10 items of 4562 documents
Generators of Random Processes in Ultrametric Spaces and Their Spectra
2009
The L 2(\( \mathbb{S} \)) space of square integrable functions on an ultrametric space \( \mathbb{S} \) has rather specific structure. As a consequence in a natural way there appear in L 2(\( \mathbb{S} \)) the operators of which unitary counterparts in L 2(ℝn) would be difficult to construct. Such class of self-adjoint operators emerge from theory of random processes on ultrametric spaces. In this paper we collect known material on spectral properties of the generators of random processes on \( \mathbb{S}_B \) an ultrametric space of sequences. (The set of p-adic numbers is a subset of \( \mathbb{S}_B \).) Then we discuss structure of the eigenspaces of the generators.
Stochastic Processes on Ends of Tree and Dirichlet Forms
2016
We present main ideas and compare two constructions of stochastic processes on the ends (leaves) of the trees with varying numbers of edges at the nods. In one of them the trees are represented by spaces of numerical sequences and the processes are obtained by solving a class of Chapman-Kolmogorov Equations. In the other the trees are described by the set of nodes and edges. To each node there is naturally associated a finite dimensional function space and the Dirichlet form on it. Having a class of Dirichlet forms at the nodes one can under certain conditions build a Dirichlet form on L2 space of funcions on the ends of the trees. We show that the state spaces of two approaches are homeomo…
Partial spreads in finite projective spaces and partial designs
1975
A partial t-spread of a projective space P is a collection 5 p of t-dimensional subspaces of P of the same order with the property that any point of P is contained in at most one element of 50. A partial t-spread 5 p of P is said to be a t-spread if each point of P is contained in an element of 5P; a partial t-spread which is not a spread will be called strictly partial. Partial t-spreads are frequently used for constructions of affine planes, nets, and Sperner spaces (see for instance Bruck and Bose [5], Barlotti and Cofman [2]). The extension of nets to affine planes is related to the following problem: When can a partial t-spread 5 ~ of a projective space P be embedded into a larger part…
Optimal Locations and Inner Products
1997
Abstract In a normed space X , we consider objective functions which depend on the distances between a variable point and the points of certain finite sets A . A point where such a function attains its minimum on X is generically called an optimal location. In this paper we obtain characterizations of inner product spaces with properties connecting optimal locations and the convex hull of A or barycenters of points of A with well chosen weights. We thus generalize several classical results about characterization of inner product spaces.
The simplex dispersion ordering and its application to the evaluation of human corneal endothelia
2009
A multivariate dispersion ordering based on random simplices is proposed in this paper. Given a R^d-valued random vector, we consider two random simplices determined by the convex hulls of two independent random samples of sizes d+1 of the vector. By means of the stochastic comparison of the Hausdorff distances between such simplices, a multivariate dispersion ordering is introduced. Main properties of the new ordering are studied. Relationships with other dispersion orderings are considered, placing emphasis on the univariate version. Some statistical tests for the new order are proposed. An application of such ordering to the clinical evaluation of human corneal endothelia is provided. Di…
Lifting paths on quotient spaces
2009
Abstract Let X be a compactum and G an upper semi-continuous decomposition of X such that each element of G is the continuous image of an ordered compactum. If the quotient space X / G is the continuous image of an ordered compactum, under what conditions is X also the continuous image of an ordered compactum? Examples around the (non-metric) Hahn–Mazurkiewicz Theorem show that one must place severe conditions on G if one wishes to obtain positive results. We prove that the compactum X is the image of an ordered compactum when each g ∈ G has 0-dimensional boundary. We also consider the case when G has only countably many non-degenerate elements. These results extend earlier work of the firs…
On norm attaining polynomials
2003
We show that for every Banach space X the set of 2-homogeneous continuous polynomials whose canonical extension to X∗∗ attain their norm is a dense subset of the space of all 2-homogeneous continuous polynomials P(2X).
Blocking sets and partial spreads in finite projective spaces
1980
A t-blocking set in the finite projective space PG(d, q) with d≥t+1 is a set $$\mathfrak{B}$$ of points such that any (d−t)-dimensional subspace is incident with a point of $$\mathfrak{B}$$ and no t-dimensional subspace is contained in $$\mathfrak{B}$$ . It is shown that | $$\mathfrak{B}$$ |≥q t +...+1+q t−1√q and the examples of minimal cardinality are characterized. Using this result it is possible to prove upper and lower bounds for the cardinality of partial t-spreads in PG(d, q). Finally, examples of blocking sets and maximal partial spreads are given.
Sigma-fragmentability and the property SLD in C(K) spaces
2009
Abstract We characterize two topological properties in Banach spaces of type C ( K ) , namely, being σ-fragmented by the norm metric and having a countable cover by sets of small local norm-diameter (briefly, the property norm-SLD). We apply our results to deduce that C p ( K ) is σ-fragmented by the norm metric when K belongs to a certain class of Rosenthal compacta as well as to characterize the property norm-SLD in C p ( K ) in case K is scattered.
Remarks on the semivariation of vector measures with respect to Banach spaces.
2007
Suppose that and . It is shown that any Lp(µ)-valued measure has finite L2(v)-semivariation with respect to the tensor norm for 1 ≤ p < ∞ and finite Lq(v)-semivariation with respect to the tensor norm whenever either q = 2 and 1 ≤ p ≤ 2 or q > max{p, 2}. However there exist measures with infinite Lq-semivariation with respect to the tensor norm for any 1 ≤ q < 2. It is also shown that the measure m (A) = χA has infinite Lq-semivariation with respect to the tensor norm if q < p.