Optimal reinsurance.
Optimal Sampling of Holomorphic Fuctions. II.
Optimal Sobolev embeddings
Optimal Sobolev embeddings on Rn.
We study Sobolev-type embeddings involving rearrangement-invariant norms. In particular, we focus on the question when such embeddings are optimal. We concentrate on the case when the functions involved are defined on Rn. This subject has been studied before, but only on bounded domains. We first establish the equivalence of the Sobolev embedding to a new type of inequality involving two integral operators. Next, we show this inequality to be equivalent to the boundedness of a certain Hardy operator...
Optimal Sobolev imbedding spaces
This paper continues our study of Sobolev-type imbedding inequalities involving rearrangement-invariant Banach function norms. In it we characterize when the norms considered are optimal. Explicit expressions are given for the optimal partners corresponding to a given domain or range norm.
Optimal stopping and impulsive control of one-dimensional diffusion processes
Optimal trend estimation in geometric asset price models
In the general geometric asset price model, the asset price P(t) at time t satisfies the relation , t ∈ [0,T], where f is a deterministic trend function, the stochastic process F describes the random fluctuations of the market, α is the trend coefficient, and σ denotes the volatility. The paper examines the problem of optimal trend estimation by utilizing the concept of kernel reproducing Hilbert spaces. It characterizes the class of trend functions with the property that the trend coefficient...
Optimality conditions for problems with set-valued objectives.
Optimality of embeddings of Bessel-potential-type spaces into generalized Hölder spaces.
We establish the sharpness of embedding theorems for Bessel-potential spaces modelled upon Lorentz-Karamata spaces and we prove the non-compactness of such embeddings. Target spaces in our embeddings are generalized Hölder spaces. As consequences of our results, we get continuous envelopes of Bessel-potential spaces modelled upon Lorentz-Karamata spaces.
Optimization of Convex function on w*-compact sets.
Optimization of Functions on Certain Subsets of Banach Spaces.
Optimization Problems for KG.
Orbites périodiques de systèmes conservatifs
Orbits in symmetric spaces, II
Suppose E is fully symmetric Banach function space on (0,1) or (0,∞) or a fully symmetric Banach sequence space. We give necessary and sufficient conditions on f ∈ E so that its orbit Ω(f) is the closed convex hull of its extreme points. We also give an application to symmetrically normed ideals of compact operators on a Hilbert space.
Orbits of linear operators and Banach space geometry
Let T be a bounded linear operator on a (real or complex) Banach space X. If (aₙ) is a sequence of non-negative numbers tending to 0, then the set of x ∈ X such that ||Tⁿx|| ≥ aₙ||Tⁿ|| for infinitely many n’s has a complement which is both σ-porous and Haar-null. We also compute (for some classical Banach space) optimal exponents q > 0 such that for every non-nilpotent operator T, there exists x ∈ X such that , using techniques which involve the modulus of asymptotic uniform smoothness of X.
Order bounded operators and tensor products of Banach lattices.
Order bounded orthosymmetric bilinear operator
It is proved by an order theoretical and purely algebraic method that any order bounded orthosymmetric bilinear operator where and are Archimedean vector lattices is symmetric. This leads to a new and short proof of the commutativity of Archimedean almost -algebras.
Order boundedness and weak compactness of the set of quasi-measure extensions of a quasi-measure
Let and be algebras of subsets of a set with , and denote by the set of all quasi-measure extensions of a given quasi-measure on to . We give some criteria for order boundedness of in , in the general case as well as for atomic . Order boundedness implies weak compactness of . We show that the converse implication holds under some assumptions on , and or alone, but not in general.
Order continuous linear functionals on non-locally convex Orlicz spaces
The space of all order continuous linear functionals on an Orlicz space defined by an arbitrary (not necessarily convex) Orlicz function is described.
Order continuous seminorms and weak compactness in Orlicz spaces.
Let L-phi be an Orlicz space defined by a Young function phi over a sigma-finite measure space, and let phi* denote the complementary function in the sense of Young. We give a characterization of the Mackey topology tau(L*,L-phi*) in terms of some family of norms defined by some regular Young functions. Next we describe order continuous (=absolutely continuous) Riesz seminorms on L-phi, and obtain a criterion for relative sigma(L-phi,L-phi*)-compactness in L-phi. As an application we get a representation...