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...

We begin this lecture by asking why should an arbitrary n × n Gaussian matrix A be invertible? That is, does there exist a lower bound on the smallest singular value s n (A) = inf x∈S n−1 Ax 2 ≥ c √ n where c > 0 is an absolute constant. There are two reasons (or cases) which we will pursue in this lecture. 1. In Lecture 15 we saw that the invertibility of rectangular (i.e., non-square) Gaussia...

Abstract The classes of band-dominated operators and the subclass in Wiener algebra $${\mathcal {W}}$$ W are known to be inverse closed. This paper studies extends partially results that type for one-sided generalized invertibility. Furthermore, invertibility, Fredholm property index independent underlying sp...

An explicit counterexample shows that contrary to the situation in the special Colombeau algebra, positivity and invertibility cannot be characterized pointwise in algebras of tempered generalized functions. Further a point value characterization of the latter is refined.

In this paper we give a representation of the Moore-Penrose inverse of a linear combination of generalized and hypergeneralized projectors. Also, we consider the invertibility of some linear combination of commuting generalized and hypergeneralized projectors.