Necessary and sufficent conditions are obtained for ¿(/-factorization of operators on /,. In particular it is shown that uniform invertibility of the compressions of the operator is not sufficient to insure an LU-factorization of the operator, thus answering a question of de Boor, Jia, and Pinkus. The question of when a bounded linear operator on lp, 1 < p <, oo, has an Li/-factorization has be...

Let us suppose T ( π, 1 2 ) ∼ √ 2 −9 + 1 ∨ · · · × 1± β 6= W (p× 1) tan−1 (−1) × · · · ∩Nq̃

This is a survey of Harold Widom’s work in Toeplitz operators, embracing his early results on the invertibility and spectral theory investigations eigenvalue distribution convolution groundbreaking research into Wiener–Hopf determinants.

An approach to the optimal design of dynamic force/torque sensors is presented. The approach is based on the system invertibility properties of the truncated normal modes representation of an elastic beam. Theoretical results are connrmed by experiment simulations.

a INRIA, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France. E-mail: [email protected] b INRIA, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France. E-mail: [email protected] c Dep. of Computing and Mathematics, Nottingham Trent University, Burton Street, Nottingham, NG1 4BU, UK, and Institute for Information Transmission Problems of Russian Academy of Science...