Nevanlinna–Pick interpolation: Pick matrices have bounded number of negative eigenvalues
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چکیده
منابع مشابه
Nevanlinna–pick Interpolation: Pick Matrices Have Bounded Number of Negative Eigenvalues
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 fu...
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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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Abstract. The following problem, originally proposed by Omladi c and Semrl [Linear Algebra Appl., 249:29{46 (1996)], is considered. Let k and n be positive integers such that k < n. Let L be a subspace of Mn(F ), the space of n n matrices over a eld F , such that each A 2 L has at most k distinct eigenvalues (in the algebraic closure of F ). Then, what is the maximal dimension of L. Omladi c an...
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The eigenvalues of the matrices that occur in certain finitedimensional interpolation problems are directly related to their well posedness and strongly depend on the distribution of the interpolation knots, that is, on the sampling set. We study this dependency as a function of the sampling set itself and give accurate bounds for the eigenvalues of the interpolation matrices. The bounds can be...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2003
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-03-07096-5