منابع مشابه
On the extension in the Hardy classes and the Nevanlinna class
Using potential theoretic methods we give extension results for functions in various Hardy classes and in the Nevanlinna class in C". Our exceptional sets are polar or slightly larger n-small sets depending whether the majorant is a harmonic or separately hyperharmonic function.
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 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...
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 کاملOn the Generalized Hardy Spaces
and Applied Analysis 3 Definition 2.1. Let F : H U → H U be a linear operator such that F f 0 if and only if f 0, that is, F is 1-1. For 1 ≤ p < ∞, the generalized Hardy space HF,p U HF,p is defined to be the collection of all analytic functions f on U for which
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ژورنال
عنوان ژورنال: Arkiv för Matematik
سال: 1976
ISSN: 0004-2080
DOI: 10.1007/bf02385825