In this paper we construct a bounded strictly positive function õ such that the Liouville property fails for the divergence form operator L ≥ r(õ2r). Since in addition ∆õÛõ is bounded, this example also gives a negative answer to a problem of Berestycki, Caffarelli and Nirenberg concerning linear Schrödinger operators.

If the Navier-Stokes equations are averaged with a local, spacial convolution type filter, φ = gδ ∗ φ , the resulting system is not closed due to the filtered nonlinear term uu. An approximate deconvolution operator D is a bounded linear operator which satisfies

Let E, F be exact operator spaces (for example subspaces of the C *-algebra K(H) of all the compact operators on an infinite dimensional Hilbert space H). We study a class of bounded linear maps u: E → F * which we call tracially bounded. In particular, we prove that every completely bounded (in short c.b.) map u: E → F * factors boundedly through a Hilbert space. This is used to show that the ...

This paper concerns the reconstruction of the absorption and scattering parameters in a time-dependent linear transport equation from full knowledge of the albedo operator at the boundary of a bounded domain of interest. We present optimal stability results on the reconstruction of the absorption and scattering parameters for a given error in the measured albedo operator.

In this paper we study some properties of the classical Arnoldi based methods for solving infinite dimensional linear equations involving compact operators. These problems are intrinsically ill-posed since a compact operator does not admit a bounded inverse. We study the convergence properties and the ability of these algorithms to estimate the dominant singular values of the operator.

Let T be a bounded linear operator on X = (Σ `q)p with 1 ≤ q < ∞ and 1 < p <∞. Then T is a commutator if and only if for all non zero λ ∈ C, the operator T − λI is not X-strictly singular.

In this talk, we discuss the maximum number of n × n pure imaginary quaternionic solutions to the Hurwitz matrix equations given by TiT ∗ j + TjT ∗ i = 2δijI, i, j = 1, . . . , p, where δij is the Kronecker delta. The numerical radius of weighted shift operators Speaker Mao-Ting Chien (Soochow University), [email protected] Co-author Hiroshi Nakazato (Hirosaki University). Abstract Let T be a ...

The classical time-invariant Hankel-norm approximation problem is generalized to the time-varying context. The input-output operator of a time-varying bounded causal linear system acting in discrete time may be specified as a bounded upper-triangular operator T with block matrix entries Tij. For such an operator T, we will define the Hankel norm as a generalization of the time-invariant Hankel ...

If Tμ is a Fourier multiplier such that μ is any (possibly unbounded) symbol with uniformly bounded q-variation on dyadic coronas, we prove that the commutator [T, Tμ] = TTμ−TμT is bounded on the Besov space B p (R ), if T is any bounded linear operator on a couple of Besov spaces Bj ,rj p (R) (j = 0, 1, and 0 < σ1 < σ < σ0).

Robust stability and performance analysis techniques are presented for time-delay systems consisting of the feedback interconnection of a linear time-delay system, with a bounded and casual linear operator. This linear operator features all the parameter and/or dynamical uncertainties excluding the delay elements. The delays considered are noncommensurate, time-invariant but uncertain, residing...