This paper studies Newton-type methods for minimization of partly smooth convex functions. Sequential Newton methods are provided using local parameterizations obtained from U -Lagrangian theory and from Riemannian geometry. The Hessian based on the U -Lagrangian depends on the selection of a dual parameter g; by revealing the connection to Riemannian geometry, a natural choice of g emerges for...

This paper studies Newton-type methods for minimization of partly smooth convex functions. Sequential Newton methods are provided using local parameterizations obtained from U-Lagrangian theory and from Riemannian geometry. The Hessian based on the ULagrangian depends on the selection of a dual parameter g; by revealing the connection to Riemannian geometry, a natural choice of g emerges for wh...

We show that the general Levy process can be embedded in a suitable Fock space, classified by cocycles of the real line regarded as a group. The formula of de Finetti corresponds to coboundaries. Kolmogorov’s processes correspond to cocycles of which the derivative is a cocycle of the Lie algebra of R. The Lévy formula gives the general cocycle. 1 Cyclic representations of groups Let G be a gro...

Abstract We prove that if G is a discrete group and $$(A,G,\alpha )$$ ( A , G α ) C*-dynamical system such the reduced crossed product $$A\rtimes _{r,\alpha } G$$ ⋊ r...

Suppose A is a Banach algebra without order. We show that an approximate multiplier T : A → A is an exact multiplier. We also consider an approximate multiplier T on a Banach algebra which need not be without order. If, in addition, T is approximately additive, then we prove the Hyers-Ulam-Rassias stability of T. 1. Introduction and statement of results. It seems that the stability problem of f...

The vector x is called supercyclic for T ifC orb T, x is dense inH. Also a supercyclic operator is one that has a supercyclic vector. For some sources on these topics, see 1–16 . Let H be a separable Hilbert space of functions analytic on a plane domain G such that, for each λ in G, the linear functional of evaluation at λ given by f → f λ is a bounded linear functional on H. By the Riesz repre...

Our main result provides a closed expression for the completely bounded Fourier multiplier norm of the spherical functions on the generalized Lorentz groups SO0(1, n) (for n ≥ 2). As a corollary, we find that there is no uniform bound on the completely bounded Fourier multiplier norm of the spherical functions on the generalized Lorentz groups. We extend the latter result to the groups SU(1, n)...

Let G be a discrete abelian group on which there is a multiplier a: GxG -* T. It is shown that if all the irreducible representations of (G, a) are induced from 1-dimensional representations of subgroups then all of the representations of (G, a) are Type I. This represents the first step in the proof of the corresponding result for arbitrary discrete nilpotent groups.

‎let $g$ be a finite $p$-group and $n$ be a normal subgroup of $g$ with‎ ‎$|n|=p^n$ and $|g/n|=p^m$‎. ‎a result of ellis (1998) shows‎ ‎that the order of the schur multiplier of such a pair $(g,n)$ of finite $p$-groups is bounded‎ ‎by $ p^{frac{1}{2}n(2m+n-1)}$ and hence it is equal to $‎ ‎p^{frac{1}{2}n(2m+n-1)-t}$ for some non-negative integer $t$‎. ‎recently‎, ‎the authors have characterized...