We consider partial differential operators H = − div(C∇) in divergence form on R with a positive-semidefinite, symmetric, matrix C of real L∞-coefficients. First, we prove that one can define H as a selfadjoint operator on L2(R ) such that the corresponding semigroup extends as a positive, contraction semigroup to all the Lp-spaces. Secondly, we establish that H is strongly elliptic if and only...

It is shown that, for the spectral operators of scalar type, the well-known characterizations of the generation of C0and analytic semigroups of bounded linear operators can be reformulated exclusively in terms of the spectrum of such operators, the conditions on the resolvent of the generator being automatically met and the corresponding semigroup being that of the exponentials of the operator.

In this paper we describe an iterative operator-splitting method for unbounded operators. We derive error bounds for iterative splitting methods in the presence of unbounded operators and semigroup operators. Here mixed applications of hyperbolic and parabolic type are allowed and discussed in the applications. Mixed experiments are applied to ordinary differential equations and evolutionary Sc...

A dynamic system with structural damping described by partial differential equations is investigated. The system is first converted to an abstract evolution equation in an appropriate Hilbert space, and the spectral and semigroup properties of the system operator are discussed. Finally, the well-posedness and the asymptotical stability of the system are obtained by means of a semigroup of linea...

We give a new criterion for asymptotic completeness in KümmererMaassen-scattering theory which is more directly in terms of the coupling. To this end we define the semigroup of dual extended transition operators. Asymptotic completeness holds if and only if this semigroup is ergodic. This may also be interpreted in terms of entanglement.

The paper deals with semigroups of operators associated with delay diierential equation: _ x(t) = Ax(t) + L 1 x(t ? h) + L 2 xt; where A is the innnitesimal generator of an analytic semigroup on a Hilbert space X and L 1 , L 2 are densely deened closed operators in X and L 2 (?h; 0;X) respectively. The adjoint semigroupof the solution semigroupof the delay diierentialequation is characterized. ...

Beasley, L.B. and N.J. Pullman, Linear operators that strongly preserve graphical properties of matrices, Discrete Mathematics 104 (1992) 143-157. An operator on the set Ju of n X n matrices strongly preserves a subset 9 if it maps 9 into 9 and A\% into A\%. The operator semigroup of 9 is the semigroup of linear operators strongly preserving 9. We show that all the n x n matrix-families which a...

The classical approach of solvability using group theory is well known and one original motivation is to solve polynomials by radicals. Radicals are square, cube, square root, cube root etc of the original coefficients for the polynomial. A polynomial is solvable by radicals if the permutation group is solvable. This is exact solvability via group theory. With modern computers, we might need to...