2,930 research outputs found
Pairs of orthogonal countable ordinals
We characterize pairs of orthogonal countable ordinals. Two ordinals
and are orthogonal if there are two linear orders and on the
same set with order types and respectively such that the
only maps preserving both orders are the constant maps and the identity map. We
prove that if and are two countable ordinals, with , then and are orthogonal if and only if either
or and
On non-coercive mixed problems for parameter-dependent elliptic operators
We consider a (generally, non-coercive) mixed boundary value problem in a
bounded domain of for a second order parameter-dependent
elliptic differential operator with complex-valued
essentially bounded measured coefficients and complex parameter . The
differential operator is assumed to be of divergent form in , the boundary
operator is of Robin type with possible pseudo-differential
components on . The boundary of is assumed to be a Lipschitz
surface. Under these assumptions the pair induces
a holomorphic family of Fredholm operators in
suitable Hilbert spaces , of Sobolev type. If the argument
of the complex-valued multiplier of the parame\-ter in is continuous and the coefficients related to second order
derivatives of the operator are smooth then we prove that the operators
are conti\-nu\-ously invertible for all with
sufficiently large modulus on each ray on the complex plane
where the differential operator is
parameter-dependent elliptic. We also describe reasonable conditions for the
system of root functions related to the family to be (doubly)
complete in the spaces , and the Lebesgue space
- …