In this article we consider the zeta regularized determinant of Laplace-type operators on the generalized cone. For arbitrary self-adjoint extensions of a matrix of singular ordinary differential operators modelled on the generalized cone, a closed expression for the determinant is given. The result involves a determinant of an endomorphism of a finite-dimensional vector space, the endomorphism...

Here we give brief account of hermitian symplectic spaces, showing that they are intimately connected to symmetric as well as self-adjoint extensions of a symmetric operator. Furthermore we find an explicit parameterisation of the Lagrange Grassmannian in terms of the unitary matrices U(n). This allows us to explicitly describe all self-adjoint boundary conditions for the Schrödinger operator o...

The theory of one-parameter semigroups provides a good entry into the study of the properties of non-self-adjoint operators and of the evolution equations associated with them. There are many situations in which such an operator A arises by linearizing some non-linear evolution equation around a stationary point. The stability of the stationary point implies that every eigenvalue of the semigro...

Abstract: The classical Weyl-von Neumann theorem states that for any selfadjoint operator A in a separable Hilbert space H there exists a (non-unique) Hilbert-Schmidt operator C = C∗ such that the perturbed operator A + C has purely point spectrum. We are interesting whether this result remains valid for non-additive perturbations by considering self-adjoint extensions of a given densely define...

approximation error A linear operator L H H on a Hilbert space H is said to be self adjoint if for all f g H hLf gi hf Lgi It is said to be positive resp strictly positive if it is self adjoint and for all non trivial f H hLf fi resp hLf fi The next result the Spectral Theorem for compact operators see Section of for a proof will be useful in this and the next chapter Theorem Let L be a compact...

We study a semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. The Schrödinger operator is a perturbation of the second quantization operator of an unbounded self-adjoint operator by a C-potential function. This result is an extension of [1].

— We study a semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. The Schrödinger operator is a perturbation of the second quantization operator of an unbounded self-adjoint operator by a C3-potential function. This result is an extension of [1].

The Kneser-Hecke-operator is a linear operator defined on the complex vector space spanned by the equivalence classes of a family of self-dual codes of fixed length. It maps a linear self-dual code C over a finite field to the formal sum of the equivalence classes of those self-dual codes that intersect C in a codimension 1 subspace. The eigenspaces of this self-adjoint linear operator may be d...

The Kneser-Hecke-operator is a linear operator defined on the complex vector space spanned by the equivalence classes of a family of self-dual codes of fixed length. It maps a linear self-dual code C over a finite field to the formal sum of the equivalence classes of those self-dual codes that intersect C in a codimension 1 subspace. The eigenspaces of this self-adjoint linear operator may be d...