We study non-autonomous observation systems , where is a strongly measurable family of closed operators on Banach space and bounded from to . Based an abstract uncertainty principle dissipation estimate, we prove that the system satisfies final-state observability estimate in for subsets present applications above result families uniformly elliptic differential as well Ornstein–Uhlenbeck with I...

We use a “weakly formulated” Sylvester equation H1/2TM−1/2 −H−1/2TM1/2 = F to obtain new bounds for the rotation of spectral subspaces of a nonnegative selfadjoint operator in a Hilbert space. Our bound extends the known results of Davis and Kahan. Another application is a bound for the square root of a positive selfadjoint operator which extends the known rule: “The relative error in the squar...

Let u(x) = s(x) + n(x) , where s(x) and n(x) are random fields, s(x) is useful signal, n(x) is noise. Assume that s(x) = n(x) = 0 , where the bar stands for mean value. Suppose that the covariance functions R(x, y) := u * (x)u(y) and f (x, y) := u * (x)s(y) are known, where the asterisk stands for complex conjugate. Assume that u(x) is observed in a bounded domain D ⊂ R r of the Euclidean space...

where E is a real elliptic linear differential operator in a bounded domain G of R” with a given system of linear homogeneous conditions, say, BX = 0 on the boundary aG of G and where N is a Nemitsky type nonnecessarily linear operator. We shall make use here of the alternative method, and particularly we shall make use for the elliptic case of new remarks. These remarks suggest that both the a...

The representations of the degenerate affine Hecke algebra in which the analogues of the Dunkl operators are given by finite-difference operators are introduced. The non-selfadjoint lattice analogues of the spin Calogero-Sutherland hamiltonians are analysed by Bethe-Ansatz. The sl(m)-Yangian representations arising from the finite-difference representations of the degenerate affine Hecke algebr...

We construct efficient approximations for the eigenfunctions of non-selfadjoint Schrödinger operators in one dimension. The same ideas also apply to the study of resonances of self-adjoint Schrödinger operators which have dilation analytic potentials. In spite of the fact that such eigenfunctions can have surprisingly complicated structures with multiple local maxima, we show that a suitable ad...

The squared Laplace operator acting on symmetric rank-two tensor fields is studied on a (flat) Riemannian manifold with smooth boundary. Symmetry of this fourth-order elliptic operator is obtained provided that such tensor fields and their first (or second) normal derivatives are set to zero at the boundary. Strong ellipticity of the resulting boundary-value problems is also proved. Mixed bound...