Interpolation in the Nevanlinna and Smirnov classes and harmonic majorants
نویسندگان
چکیده
منابع مشابه
Interpolation in the Nevanlinna Class and Harmonic Majorants
We consider a free interpolation problem in Nevanlinna and Smirnov classes and find a characterization of the corresponding interpolating sequences in terms of the existence of harmonic majorants of certain functions. We also consider the related problem of characterizing positive functions in the disc having a harmonic majorant. An answer is given in terms of a dual relation which involves pos...
متن کاملInterpolation 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...
متن کاملInterpolating Sequences for the Nevanlinna and Smirnov Classes
We give analytic Carleson-type characterisations of the interpolating sequences for the Nevanlinna and Smirnov classes. From this we deduce necessary and sufficient geometric conditions, both expressed in terms of a certain non-tangential maximal function associated to the sequence. Some examples show that the gap between the necessary and the sufficient conditions cannot be covered. We also di...
متن کاملInterpolation and harmonic majorants in big Hardy-Orlicz spaces
Free interpolation in Hardy spaces is characterized by the well-known Carleson condition. The result extends to Hardy-Orlicz spaces contained in the scale of classical Hardy spaces H, p > 0. For the Smirnov and the Nevanlinna classes, interpolating sequences have been characterized in a recent paper in terms of the existence of harmonic majorants (quasi-bounded in the case of the Smirnov class)...
متن کاملMultiple 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...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2004
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2004.02.015