132 research outputs found
Factorization method and general second order linear difference equation
This paper addresses an investigation on a factorization method for
difference equations. It is proved that some classes of second order linear
difference operators, acting in Hilbert spaces, can be factorized using a pair
of mutually adjoint first order difference operators. These classes encompass
equations of hypergeometic type describing classical orthogonal polynomials of
a discrete variable
Integrable Systems Related to Deformed
We investigate a family of integrable Hamiltonian systems on Lie-Poisson
spaces dual to Lie algebras being two-parameter deformations of . We
integrate corresponding Hamiltonian equations on and
by quadratures as well as discuss their possible physical
interpretation
Integrable Hamiltonian systems related to the Hilbert--Schmidt ideal
By application of the coinduction method as well as Magri method to the ideal
of real Hilbert-Schmidt operators we construct the hierarchies of integrable
Hamiltonian systems on the Banach Lie-Poisson spaces which consist of these
type of operators. We also discuss their algebraic and analytic properties as
well as solve them in dimensions N=2,3,4.Comment: 36 page
Cyclic Lie-Rinehart algebras
We study Lie-Rinehart algebra structures in the framework provided by a
duality pairing of modules over a unital commutative associative algebra. Thus,
we construct examples of Lie brackets corresponding to a fixed anchor map whose
image is a cyclic submodule of the derivation module, and therefore we call
them cyclic Lie-Rinehart algebras. In a very special case of our construction,
these brackets turn out to be related to certain differential operators that
occur in mathematical physics.Comment: 17 page
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