Heinz Langer

A factorization result for generalized Nevanlinna functions of the class N-k

AbstractLetQ∈Nk. It is shown that if α is a nonreal pole or a real generalized pole of nonpositive type and β is a nonreal zero or a real generalized zero of nonpositive type of the functionQ then the function

Self-adjoint operators with inner singularities and pontryagin spaces

Q_1 (z): = \frac{{(z - \alpha )(z - \bar \alpha )}}{{(z - \beta )(z - \bar \beta )}}Q(z)

Hamiltonian Systems with Eigenvalue Depending Boundary Conditions

belongs to the classNk−1.

Direct and inverse spectral problems for generalized strings

Recall ([1], [2], [3]) that Nκ denotes the set of all complex valued functions Q which are meromorphic in the open upper half plane C + and such that the kernel NQ:

Remarks on the perturbation of analytic matrix functions III

{N_Q}\left( {z,\zeta } \right):\left( {Q\left( z \right) - \overline {Q\left( \zeta \right)} } \right)/\left( {z - \overline \zeta } \right)

Variational principles for real eigenvalues of self-adjoint operator pencils

(1.1) for z,ζ e D Q has κ negative squares (here D Q (⊂C +) denotes the domain of holomorphy of Q). This means that for arbitrary n e Z and z1,z2,...,zn e D Q the matrix (NQ(zi,zj)) 1 n has at most κ negative eigenvalues and for at least one choice of n, z1,...,zn it has exactly κ negative eigenvalues. The class No coincides with the Nevanlinna class of all functions which are holomorphic in C + and map C + into C + UR. The following two examples of functions of the class N1 were considered in [2], [4], respectively: