On Factorizations of Selfadjoint Ordinary Differential Operators

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

Spectrality of Ordinary Differential Operators

We prove the long standing conjecture in the theory of two-point boundary value problems that completeness and Dunford’s spectrality imply Birkhoff regularity. In addition we establish the even order part of S.G.Krein’s conjecture that dissipative differential operators are Birkhoff-regular and give sharp estimate of the norms of spectral projectors in the odd case. Considerations are based on ...

Bispectral algebras of commuting ordinary differential operators

We develop a systematic way for constructing bispectral algebras of commuting ordinary differential operators of any rank N . It combines and unifies the ideas of Duistermaat–Grünbaum and Wilson. Our construction is completely algorithmic and enables us to obtain all previously known classes or individual examples of bispectral operators. The method also provides new broad families of bispectra...

On the Approximation of Isolated Eigenvalues of Ordinary Differential Operators

We extend a result of Stolz and Weidmann on the approximation of isolated eigenvalues of singular Sturm–Liouville and Dirac operators by the eigenvalues of regular operators.

Multistep Filtering Operators for Ordinary Differential Equations

Interval methods for ordinary di erential equations (ODEs) provide guaranteed enclosures of the solutions and numerical proofs of existence and unicity of the solution. Unfortunately, they may result in large over-approximations of the solution because of the loss of precision in interval computations and the wrapping e ect. The main open issue in this area is to nd tighter enclosures of the so...