Nevanlinna–pick Interpolation: Pick Matrices Have Bounded Number of Negative Eigenvalues
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چکیده
The Nevanlinna–Pick interpolation problem is studied in the class of functions defined on the unit disk without a discrete set, with the property that all their Pick matrices have not more than a prescribed number of negative eigenvalues. It is shown, in particular, that the degenerate problem always has a unique solution, not necessarily meromorphic. A related extension problem to a maximal function in the class is also studied.
منابع مشابه
Ju n 20 02 Functions with Pick matrices having bounded number of negative eigenvalues
A class is studied of complex valued functions defined on the unit disk (with a possible exception of a discrete set) with the property that all their Pick matrices have not more than a prescribed number of negative eigenvalues. Functions in this class, known to appear as pseudomultipliers of the Hardy space, are characterized in several other ways. It turns out that a typical function in the c...
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تاریخ انتشار 2003