Subspace identification is a classical and very well studied problem in system identification. The problem was recently posed as a convex optimization problem via the nuclear norm relaxation. Inspired by robust PCA, we extend this framework to handle outliers. The proposed framework takes the form of a convex optimization problem with an objective that trades off fit, rank and sparsity. As in r...

We study a nonlinear initial value Cauchy problem depending upon a complex perturbation parameter with vanishing initial data at complex time t = 0 and whose coefficients depend analytically on ( , t) near the origin in C and are bounded holomorphic on some horizontal strip in C w.r.t the space variable. This problem is assumed to be non-Kowalevskian in time t, therefore analytic solutions at t...

have been given previously by B iedenharn and B latt l , and by D elves 2. The variation principle of B iedenharn and Blatt requires trial functions for a complete set of eigenfunctions and is therefore of a rather complicated nature. D elves succeeded in reducing the number of trial functions to two, yjQT(f*) and ipm (r), but his principle determines only the square of the wave function. Moreo...

We address the question of which function spaces are invariant under the action of scalar conservation laws in one and several space dimensions. We establish two types of results. The rst result shows that if the initial data is in a rearrangement-invariant function space, then the solution is in the same space for all time. Secondly, we examine which smoothness spaces among the Besov spaces ar...

In the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. In particular, it isshown that the Cauchy-Schwarz inequality holds. Moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy Hilbert space has a complementary subspace.Finally, the notions of fuzzy bo...

We give upper bounds on the Walsh coefficients of functions for which the derivative of order at least one has bounded variation of fractional order. Further, we also consider the Walsh coefficients of functions in periodic and non-periodic reproducing kernel Hilbert spaces. A lower bound which shows that our results are best possible is also shown. Mathematical Subject Classification (2000): P...

Let $X$ be a Banach space of $dim X > 2$ and $B(X)$ be the space of bounded linear operators on X. If $L : B(X)to B(X)$ be a Lie higher derivation on $B(X)$, then there exists an additive higher derivation $D$ and a linear map $tau : B(X)to FI$ vanishing at commutators $[A, B]$ for all $A, Bin B(X)$ such that $L = D + tau$.

In this work we propose a definition of comonotonicity for elements ofB (H)sa, i.e., bounded self-adjoint operators defined over a complex Hilbert space H. We show that this notion of comonotonicity coincides with a form of commutativity. Intuitively, comonotonicity is to commutativity as monotonicity is to bounded variation. We also define a notion of Choquet expectation for elements of B (H)s...

This paper studies the behavior under iteration of the maps Tab(x, y) = (Fab(x)−y, x) of the plane R2, in which Fab(x) = ax if x ≥ 0 and bx if x < 0. This family of piecewise-linear maps has the parameter space (a, b) ∈ R2. These maps are area-preserving homeomorphisms of R2 that map rays from the origin into rays from the origin. The orbits of the map are solutions of the nonlinear difference ...

Abstract: Pole assignment by feedback control of the second order coupled singular distributed parameter systems is discussed via functional analysis and operator theory in Hilbert space. The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator. This research is theoretically important for studying the stab...