On Algebraically Integrable Differential Operators on an Elliptic Curve

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Asymptotic distribution of eigenvalues of the elliptic operator system

Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.

The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...

Abelian solitons

We describe a new algebraically completely integrable system, whose integral manifolds are co-elliptic subvarieties of Jacobian varieties. This is a multi-periodic extension of the Krichever-Treibich-Verdier system, which consists of elliptic solitons. The goal of this work is to generalize the theory of elliptic solitons, which was developed by A. Treibich and J.-L. Verdier based on earlier wo...

Heckman-opdam Hypergeometric Functions and Their Specializations

is completely integrable and hence L(k) is in a commuting system of differential operators with n algebraically independent operators. Then we have the following fundamental result (cf. [1]). Theorem [Heckman, Opdam]. When kα are generic, the function F (λ, k;x) has an analytic extension on R and defines a unique simultaneous eigenfunction of the commuting system of differential operators with ...