https://ogma.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 Convex analysis in groups and semigroups: a sampler https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:35977 Wed 22 Jan 2020 12:27:08 AEDT ]]> On the geometry of projective tensor products https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:34825 1 ≤ ... ≤ pk ≤ ∞ .]]> Wed 15 May 2019 14:17:20 AEST ]]> A Lyapunov Function Construction for a Non-convex Douglas-Rachford Iteration https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:42729 Thu 22 Jun 2023 11:58:43 AEST ]]> Improved bounds in the metric cotype inequality for Banach spaces https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:31587 q then for every integer n there exists an even integer m≲n 1+1/q such that for every f:Z n/m → X we have [formula could not be replicated] where the expectations are with respect to uniformly chosen x∈Zn/m and ε∈{-1,0,1}n, and all the implied constants may depend only on q, and the Rademacher cotype q constant of X. This improves the bound of m≲n2+1/q from Mendel and Naor (2008). The proof of (1) is based on a "smoothing and approximation" procedure which simplifies the proof of the metric characterization of Rademacher cotype of Mendel and Naor (2008). We also show that any such "smoothing and approximation" approach to metric cotype inequalities must require m≳n 1/2 + 1/q.]]> Sat 24 Mar 2018 08:44:59 AEDT ]]> Small ball estimates for quasi-norms https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:28414 Sat 24 Mar 2018 07:35:59 AEDT ]]> Nearest points and delta convex functions in Banach spaces https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:24006 C in a Banach space (X, || · ||), a point x ∈ X is said to have a nearest point in C if there exists z ∈ C such that dC(x) = ||x - z||, where dC is the distance of x from C. We survey the problem of studying the size of the set of points in X which have nearest points in C. We then turn to the topic of delta convex functions and indicate how it is related to finding nearest points.]]> Sat 24 Mar 2018 07:16:42 AEDT ]]> Some remarks on convex analysis in topological groups https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:25161 Sat 24 Mar 2018 07:14:30 AEDT ]]> Inverse Littlewood-Offord problems for quasi-norms https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:34275 d, n vectors v1,…,vn∈ℝd, a number R > 0, and i.i.d. random variables η1,…,ηn, we study the geometric and arithmetic structure of the multi-set V = {v1,…,vn} under the assumption that the concentration function [formula could not be replicated] does not decay too fast as n → ∞. This generalises the case where K is the Euclidean ball, which was previously studied in Nguyen and Vu (Adv Math 226(6):5298–5319, 2011) and Tao and Vu (Combinatorica 32(3):363–372, 2012), to the non-Euclidean settings, that is, to general norms and quasi-norms in ℝd.]]> Mon 25 Feb 2019 14:55:27 AEDT ]]> A Remark on the Convergence of the Douglas-Rachford Iteration in a Non-convex Setting https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:42879 Fri 23 Jun 2023 09:43:44 AEST ]]> A Perron-Frobenius type result for integer maps and applications https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:45451 Fri 11 Aug 2023 12:16:35 AEST ]]>