Symmetric and Ordinary Differentiation

Spectral properties of non - symmetric systems of ordinary differential operators

On skew-symmetric differentiation matrices

The theme of this paper is the construction of finite-difference approximations to the first derivative in the presence of Dirichlet boundary conditions. Stable implementation of splitting-based discretisation methods for the convectiondiffusion equation requires the underlying matrix to be skew symmetric and this turns out to be a surprisingly restrictive condition. We prove that no skewsymmet...

Symmetric differentiation on time scales

While the functions in (1.1) do not have ordinary derivatives at t = 0, they have symmetric derivatives: f s (0) = g (0) = h (0) = 0. For a deeper understanding of the symmetric derivative and its properties, we refer the reader to the specialized monograph [8]. Here we note that the symmetric quotient (f (t+ h)− f (t− h)) /(2h) has, in general, better convergence properties than the ordinary d...

Symmetric module and Connes amenability

In this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric Connes amenability. We determine symmetric module amenability and symmetric Connes amenability of some concrete Banach algebras. Indeed, it is shown that $ell^1(S)$ is  a symmetric $ell^1(E)$-module amenable if and only if $S$ is amenable, where $S$ is an inverse semigroup with subsemigr...

A Krein Space Approach to Symmetric Ordinary Differential Operators with an Indefinite Weight Function

l(f)=(-l)“(Pof’“‘)‘“‘+(-l)“-‘(p,f’”-”)’”~”+ ... +p,f=A.rf (0.1) on a finite or infinite interval (a, b) with real, locally summable coefficients l/PO,Pl, ..-3 Pnv r under the assumptions that p0 >O and that the weight function r changes its sign on (a, b). If r is positive, problem (0.1) can be studied in the context of Hermitian and self-adjoint operators in the Hilbert space L*(r) with the in...