Abstract. Let G be a group of orthogonal transformations of a real Hilbert space H. Let R and W be bounded G-stable subsets ofH. Let ‖.‖R be the seminorm onH defined by ‖x‖R := supr∈R |〈r, x〉| for x ∈ H. We show that if W is weakly compact and the orbit space R/G is compact for each k ∈ N, then the orbit space W/G is compact when W is equiped with the norm topology induced by ‖.‖R. As a consequ...

We consider estimating an unknown signal, which is both blocky and sparse, corrupted by additive noise. We study three interrelated least squares procedures and their asymptotic properties. The first procedure is the fused lasso, put forward by Friedman et al. (2007), which we modify into a different estimator, called the fused adaptive lasso, with better properties. The other two estimators we...

Robust dynamic programming (robust DP) mitigates the effects of ambiguity in transition probabilities on the solutions of Markov decision problems. We consider the computation of robust DP solutions for discrete-stage, infinite-horizon, discounted problems with finite state and action spaces. We present robust modified policy iteration (RMPI) and demonstrate its convergence. RMPI encompasses bo...

This article deals with a first-order least-squares approach to the solution of an optimal control problem governed by Stokes equations. As with our earlier work on a velocity control by the Stokes flow in [S. Ryu, H.-C. Lee and S. D. Kim, SIAM J. Numer. Anal., 47 (2009), pp. 1524-1545], we recast the objective functional as a H1 seminorm in the velocity control term. By introducing a velocity-...

We study Γ-convergence of graph-based Ginzburg–Landau functionals, both the limit for zero diffusive interface parameter ε → 0 and the limit for infinite nodes in the graph m→∞. For general graphs we prove that in the limit ε → 0 the graph cut objective function is recovered. We show that the continuum limit of this objective function on 4-regular graphs is related to the total variation semino...

For a closed cocompact subgroup Γ of a locally compact group G, given a compact abelian subgroup K of G and a homomorphism ρ : K̂ → G satisfying certain conditions, Landstad and Raeburn constructed equivariant noncommutative deformations C∗(Ĝ/Γ, ρ) of the homogeneous space G/Γ, generalizing Rieffel’s construction of quantum Heisenberg manifolds. We show that when G is a Lie group and G/Γ is conn...

such that (i) |0| = 0, (ii) |x| ≥ 0, for all x ∈ X , (iii) |− x| = |x|, for all x ∈ X , (iv) |x+ y| ≤ |x|+ |y|, for all x, y ∈ X , (v) if tk ∈ F, |tk − t| → 0, and xk, x ∈ X , |xk − x| → 0, then |tkxk − tx| → 0. If | · | satisfies only properties (i) to (iv), then we call | · | a near quasinorm. If the quasinorm satisfies |x| = 0 if and only if x = 0, then it is said to be total. A quasinormed ...

s of Invited Talks Alexandru Aleman, Lund University Derivation-invariant subspaces of C∞ Abstract: One motivation for the study of invariant subspaces of the differentiation operator d dx on the locally convex spaces C∞(a, b) is the fact that, as opposed to differentiation on the space of entire functions, the so-called property of spectral synthesis fails dramatically in this context. Not onl...

This paper is devoted to the maximal L1 regularity and asymptotic behavior for solutions inhomogeneous incompressible Navier-Stokes equations under a scaling-invariant smallness assumption on initial velocity. We obtain new global L1-in-time estimate Lipschitz seminorm of velocity field without any density fluctuation. In derivation this estimate, we study linear Stokes system with variable coe...

We consider a Poisson boundary value problem and its functional a posteriori error estimate derived by S. Repin in 1999. The estimate majorizes the H1 seminorm of the error of the discrete solution computed by FEM method and contains a free ux variable from the H div space. In order to keep the estimate sharp, a procedure for the minimization of the majorant term with respect to the ux variable...