Minimal spectral functions of an ordinary differential operator

Reflectionless Potentials for an Ordinary Differential Operator of Order Four

The aim of this paper is to construct exact formulae for reflectionless potentials for ordinary differential operators of order four. They lead to soliton type solutions which are well known for one dimensional Schrödinger operators. Such solitons are solutions of some non-linear integrable systems appeared in [8] (see also [9]).

Bi-concave Functions Defined by Al-Oboudi Differential Operator

The purpose of the present paper is to introduce a class $D_{Sigma ;delta }^{n}C_{0}(alpha )$ of bi-concave functions defined by Al-Oboudi differential operator. We find estimates on the Taylor-Maclaurin coefficients $leftvert a_{2}rightvert $ and $leftvert a_{3}rightvert$ for functions in this class. Several consequences of these results are also pointed out in the form of corollaries.

Ordinary differential equations with inverted functions

Equations with differentials relating to the inverse of an unknown function rather than to the unknown function itself are solved exactly for some special cases and numerically for the general case. Invertibility combined with differentiability over connected domains forces solutions always to be monotone. Numerical function inversion is key to all solution algorithms which either are of a forw...

Spectral properties of non - symmetric systems of ordinary differential operators

Differential Operator Specializations of Noncommutative Symmetric Functions

Let K be any unital commutative Q-algebra and z = (z1, · · · , zn) commutative or noncommutative free variables. Let t be a formal parameter which commutes with z and elements of K. We denote uniformly by K〈〈z〉〉 and K[[t]]〈〈z〉〉 the formal power series algebras of z over K and K[[t]], respectively. For any α ≥ 1, let D〈〈z〉〉 be the unital algebra generated by the differential operators of K〈〈z〉〉 ...