# Vol. 6 (2000), no. 3

### The second regularized trace formula for the Sturm-Liouville problem with spectral parameter in a boundary condition

E. Adigüzelov, I. Albayrak, M. Bayramoğlu

Methods Funct. Anal. Topology **6** (2000), no. 3, 1-8

### $J$-unitary nodes with strongly regular $J$-inner characteristic matrix functions

Methods Funct. Anal. Topology **6** (2000), no. 3, 9-23

### Generalized resolvents of symmetric operators and admissibility

H. S. V. de Snoo, V. A. Derkach, S. Hassi, M. M. Malamud

↓ Abstract

Methods Funct. Anal. Topology **6** (2000), no. 3, 24-55

Let A be a symmetric linear operator (or relation) with equal, possibly infinite, defect numbers. It is well know that one can associate with A a boundary value space and the Weyl function M(λ). The authors show that certain fractional-linear transforms of M(λ) are identified as Weyl functions of extensions of A, and vice versa. This connection is applied to various problems arising in the extension theory of symmetric operators. Some new criteria for a linear operator to be selfadjoint are established. When the defect numbers of A are finite the structure of all selfadjoint extensions with an exit space is completely characterized via a pair of boundary value spaces and their respective Weyl functions. New admissibility criteria are given which guarantee that a generalized resolvent of a nondensely defined symmetric operator corresponds to a selfadjoint operator extension.

### The nonstandard deformation $U'_q(so_n)$ for $q$ a root of unity

Methods Funct. Anal. Topology **6** (2000), no. 3, 56-71

### Generalized resolvents of isometric linear relations in Pontryagin spaces, II: Krein-Langer formula

Methods Funct. Anal. Topology **6** (2000), no. 3, 72-96

### Stability of special class of $q_{ij}$-CCR and extensions of irrational rotation algebras

Methods Funct. Anal. Topology **6** (2000), no. 3, 97-104