Results 31 to 40 of about 129,728 (246)

Operator Lipschitz functions on Banach spaces

, 2016
Let $X$, $Y$ be Banach spaces and let $\mathcal{L}(X,Y)$ be the space of bounded linear operators from $X$ to $Y$. We develop the theory of double operator integrals on $\mathcal{L}(X,Y)$ and apply this theory to obtain commutator estimates of the form $\
Rozendaal, Jan, Sukochev, Fedor, Tomskova, Anna   +2 more
core   +1 more source

Lattices of Lipschitz functions [PDF]

Pacific Journal of Mathematics, 1994
Let \(M\) be a metric space. We observe that \(\text{Lip}(M)\) has a striking lattice structure: its closed unit ball is lattice-complete and completely distributive. This motivates further study into the lattice structure of \(\text{Lip}(M)\) and its relation to \(M\).
openaire   +2 more sources

“It Is Much Safer to Be Sparse than Connected”: Safe Control of Robotic Swarm Density Dynamics with PDE Optimization with State Constraints

Advanced Intelligent Systems, EarlyView.
This paper proposes a novel control framework to ensure safety of a robotic swarm. A feedback optimization controller is capable of driving the swarm toward a target density while keeping risk‐zone exposure below a safety threshold. Theory and experiments show how safety is more effectively achieved for sparsely connected swarms.
Longchen Niu, Gennaro Notomista
wiley   +1 more source

JACOBI TRANSFORM OF \((\nu, \gamma, p)\)-JACOBI–LIPSCHITZ FUNCTIONS IN THE SPACE \(\mathrm{L}^{p}(\mathbb{R}^{+},\Delta_{(\alpha,\beta)}(t) dt)\)

Ural Mathematical Journal, 2019
Using a generalized translation operator, we obtain an analog of Younis' theorem [Theorem 5.2, Younis M.S. Fourier transforms of Dini–Lipschitz functions, Int. J. Math. Math. Sci., 1986] for the Jacobi transform for functions from the \((\nu, \gamma, p)\)
Mohamed El Hamma, Hamad Sidi Lafdal, Nisrine Djellab, Chaimaa Khalil   +3 more
doaj   +1 more source

A goodness‐of‐fit test for regression models with discrete outcomes

Canadian Journal of Statistics, EarlyView.
Abstract Regression models are often used to analyze discrete outcomes, but classical goodness‐of‐fit tests such as those based on the deviance or Pearson's statistic can be misleading or have little power in this context. To address this issue, we propose a new test, inspired by the work of Czado et al.
Lu Yang, Christian Genest, Johanna G. Nešlehová   +2 more
wiley   +1 more source

Extensions of semi-Lipschitz functions on quasi-metric spaces

Journal of Numerical Analysis and Approximation Theory, 2001
The aim of this note is to prove an extension theorem for semi-Lipschitz real functions dened on quasi-metric spaces, similar to McShane extension theorem for real-valued Lipschitz functions dened on a metric space ([2], [4]).
Costică Mustăţa
doaj   +2 more sources

An extension of the quasi-Newton method for minimizing locally Lipschitz functions [PDF]

Iranian Journal of Numerical Analysis and Optimization, 2019
We present a method to minimize locally Lipschitz functions. At first, a local quadratic model is developed to approximate a locally Lipschitz function. This model is constructed by using the ϵ-subdifferential.
Z. Akbari
doaj   +1 more source

Lipschitz-free spaces over compact subsets of superreflexive spaces are weakly sequentially complete

, 2017
Let $M$ be a compact subset of a superreflexive Banach space. We prove that the Lipschitz-free space $\mathcal{F}(M)$, the predual of the Banach space of Lipschitz functions on $M$, has the Pe{\l}czy\'nski's property ($V^\ast$).
Aharoni, Bourgain, Bourgain, Bourgain, Bretagnolle, Cepedello-Boiso, Cúth, Cúth, Dalet, Deville, Dutrieux, Enflo, Enflo, Enflo, Eva Pernecká, Fabian, Figiel, Figiel, Godard, Godefroy, Godefroy, Godefroy, Godefroy, Harmand, Hájek, Hájek, Hájek, James, James, Kalton, Kaufmann, Lafforgue, Lindenstrauss, McShane, Naor, Petitjean, Pełczyński, Pisier, Schoenberg, Tomasz Kochanek, Weaver, Weaver, Wojtaszczyk   +42 more
core   +1 more source

Self‐Similar Blowup for the Cubic Schrödinger Equation

Communications on Pure and Applied Mathematics, EarlyView.
ABSTRACT We give a rigorous proof for the existence of a finite‐energy, self‐similar solution to the focusing cubic Schrödinger equation in three spatial dimensions. The proof is computer‐assisted and relies on a fixed point argument that shows the existence of a solution in the vicinity of a numerically constructed approximation.
Roland Donninger, Birgit Schörkhuber
wiley   +1 more source

Meromorphic Lipschitz functions [PDF]

Bulletin of the Australian Mathematical Society, 1988
Let f be a function meromorphic in D = {|z| < 1} and let X be the chordal distance on the Riemann sphere. Then f satisfies the Lipschitz conditionin D if and only if |f′(z)|/(1 + |f(z)|2) = O((1 – |z|)α−1) and |z| → 1.
openaire   +1 more source