نتایج جستجو برای: dini lipschitz functions
تعداد نتایج: 503360 فیلتر نتایج به سال:
The primary goal of this paper is to furnish an alternative description for the contingent normal cone, similar to the one that exists for the Fréchet one, but by using a directional convergence in place of the usual one. In fact, we actually prove that the same description is available not only for the contingent normal cone, but also for the Dini-Hadamard normal cone and the Dini-Hadamard-lik...
We prove a quantitative version of the following statement. Given a Lipschitz function f from the k-dimensional unit cube into a general metric space, one can be decomposed f into a finite number of BiLipschitz functions f |Fi so that the k-Hausdorff content of f([0, 1] r ∪Fi) is small. We thus generalize a theorem of P. Jones [Jon88] from the setting of R to the setting of a general metric spa...
In this paper we address some of the most fundamental questions regarding the diierentiability structure of locally Lipschitz functions deened on Banach spaces. For example, we examine the relationship between inte-grability, D-representability and strict diierentiability. In addition to this, we show that on a large class of Banach spaces there is a signiicant family of locally Lipschitz funct...
We prove that if f is a Lipschitz function on R, A and B are self-adjoint operators such that rank(A − B) = 1, then f(A) − f(B) belongs to the weak space S1,∞, i.e., sj(A − B) ≤ const(1 + j). We deduce from this result that if A − B belongs to the trace class S1 and f is Lipschitz, then f(A) − f(B) ∈ SΩ, i.e., Pn j=0 sj(f(A) − f(B)) ≤ const log(2 + n). We also obtain more general results about ...
We study functions on topometric spaces which are both (metrically) Lipschitz and (topologically) continuous, using them in contexts where, in classical topology, ordinary continuous functions are used. We study the relations of such functions with topometric versions of classical separation axioms, namely, normality and complete regularity, as well as with completions of topometric spaces. We ...
The goal of this article is to develop a framework for large margin classification in metric spaces. We want to find a generalization of linear decision functions for metric spaces and define a corresponding notion of margin such that the decision function separates the training points with a large margin. It will turn out that using Lipschitz functions as decision functions, the inverse of the...
The SOS response, a set of cellular phenomena exhibited by eubacteria, is initiated by various causes that include DNA damage-induced replication arrest, and is positively regulated by the co- protease activity of RecA. Escherichia coli DinI, a LexA-regulated SOS gene product, shuts off the initiation of the SOS response when overexpressed in vivo. Biochemical and genetic studies indicated that...
in this paper, using a generalized dunkl translation operator, we obtain an analog of titchmarsh's theorem for the dunkl transform for functions satisfying the lipschitz-dunkl condition in $mathrm{l}_{2,alpha}=mathrm{l}_{alpha}^{2}(mathbb{r})=mathrm{l}^{2}(mathbb{r}, |x|^{2alpha+1}dx), alpha>frac{-1}{2}$.
In this paper, we study weighted composition operators between Lipschitz algebras of complex-valued bounded functions on metric spaces, not necessarily compact. We give necessary and sufficient conditions for the injectivity and the surjectivity of these operators. We also obtain sufficient and necessary conditions for a weighted composition operator between these spaces to be compact.
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