166 research outputs found
Green's formula and theorems on complete collection of isomorphisms for general elliptic boundary value problems for Douglis-Nirenberg systems
This work has been partially supported by Grant INTAS-94-2187
General-type discrete self-adjoint Dirac systems: explicit solutions of direct and inverse problems, asymptotics of Verblunsky-type coefficients and stability of solving inverse problem
We consider discrete self-adjoint Dirac systems determined by the potentials
(sequences) such that the matrices are positive definite and
-unitary, where is a diagonal matrix and has entries
and entries () on the main diagonal. We construct
systems with rational Weyl functions and explicitly solve inverse problem to
recover systems from the contractive rational Weyl functions. Moreover, we
study the stability of this procedure. The matrices (in the potentials)
are so called Halmos extensions of the Verblunsky-type coefficients .
We show that in the case of the contractive rational Weyl functions the
coefficients tend to zero and the matrices tend to the indentity
matrix .Comment: This paper is a generalization and further development of the topics
discussed in arXiv:math/0703369, arXiv:1206.2915, arXiv:1508.07954,
arXiv:1510.0079
Discrete Dirac system: rectangular Weyl functions, direct and inverse problems
A transfer matrix function representation of the fundamental solution of the
general-type discrete Dirac system, corresponding to rectangular Schur
coefficients and Weyl functions, is obtained. Connections with Szeg\"o
recurrence, Schur coefficients and structured matrices are treated.
Borg-Marchenko-type uniqueness theorem is derived. Inverse problems on the
interval and semiaxis are solved.Comment: Section 2 is improved in the second version: some new results on
Halmos extension are added and arguments are simplifie
Geographic variation of life-history traits in the sand lizard, Lacerta agilis: testing Darwin's facundity-advantage hypothesis
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