Multiple point interpolation in Nevanlinna classes

Multiple Point Interpolation in Nevanlinna Classes

has at most π positive (ν negative) squares, and that for some choice of n and z1, . . . , zn this upper bound is attained. If there is no upper bound for the number of positive (negative) squares of the forms (1) put π = ∞ (ν = ∞). We consider only such classes N πν where at least one index is finite. Denote by N ν the union N ν = ⋃ ∞ π=0 N π ν where ν is finite. A multiple point interpolation...

Interpolation Problem in Nevanlinna Classes

The abstract interpolation problem (AIP) in the Schur class was posed V. Katznelson, A. Kheifets and P. Yuditskii in 1987 as an extension of the V.P. Potapov’s approach to interpolation problems. In the present paper an analog of the AIP for Nevanlinna classes is considered. The description of solutions of the AIP is reduced to the description of L-resolvents of some model symmetric operator as...

Nevanlinna - Pick Interpolation For

We study the Nevanlinna-Pick problem for a class of subalgebras of H∞. This class includes algebras of analytic functions on embedded disks, the algebras of finite codimension in H∞ and the algebra of bounded analytic functions on a multiply connected domain. Our approach uses a distance formula that generalizes Sarason’s [18] work. We also investigate the difference between scalar-valued and m...

Parametric Nevanlinna-Pick Interpolation Theory

We consider the robust control problem for the system with real uncertainty. This type of problem can be represented with some parameters varying between the boundaries and is formulated as parametric Nevanlinna-Pick interpolation problem in this paper. The existence of a solution for such interpolation problem depends on the positivity of the corresponding Pick matrix with elements belonging t...

Nevanlinna-pick Interpolation: the Degenerated Case