Maximal Accretive Extensions of Schrödinger Operators on Vector Bundles over Infinite Graphs

Differential operators on equivariant vector bundles over symmetric spaces

Generalizing the algebra of motion-invariant differential operators on a symmetric space we study invariant operators on equivariant vector bundles. We show that the eigenequation is equivalent to the corresponding eigenequation with respect to the larger algebra of all invariant operators. We compute the possible eigencharacters and show that for invariant integral operators the eigencharacter...

Group Extensions over Infinite Words

We construct an extension E(A,G) of a given group G by infinite nonArchimedean words over an discretely ordered abelian group like Z. This yields an effective and uniform method to study various groups that ”behave like G”. We show that the Word Problem for f.g. subgroups in the extension is decidable if and only if and only if the Cyclic Membership Problem in G is decidable. The present paper ...

Vector bundles over algebraic curves

Ju l 2 00 6 Schrödinger operators on zigzag graphs

We consider the Schrödinger operator on zigzag graphs with a periodic potential. The spectrum of this operator consists of an absolutely continuous part (intervals separated by gaps) plus an infinite number of eigenvalues with infinite multiplicity. We describe all compactly supported eigenfunctions with the same eigenvalue. We define a Lyapunov function, which is analytic on some Riemann surfa...

Φ-strongly Accretive Operators

Suppose that X is an arbitrary real Banach space and T : X → X is a Lipschitz continuous φ-strongly accretive operator or uniformly continuous φ-strongly accretive operator. We prove that under different conditions the three-step iteration methods with errors converge strongly to the solution of the equation Tx = f for a given f ∈ X.