On the Takagi interpolation problem
نویسندگان
چکیده
منابع مشابه
On the Takagi interpolation problem
This problem is a generalization of the tangential Takagi interpolation problem with simple multiplicities (in the following abbreviated with TIP), which was first studied in [20] as an extension of the well-known Nevanlinna-Pick interpolation problem (see [4, 14, 16, 18]). The TIP and the closely related Nudel‘man problem have been posed and solved following various approaches: in the discrete...
متن کاملThe Takagi problem on the disk and bidisk
We give a new proof on the disk that a Pick problem can be solved by a rational function that is unimodular on the unit circle and for which the number of poles inside the disk is no more than the number of non-positive eigenvalues of the Pick matrix. We use this method to find rational solutions to Pick problems on the bidisk. Dedicated to the memory of Bela Szokefalvi-Nagy, whose work inspire...
متن کاملBoundary Concentrations on Segments for the Lin-ni-takagi Problem
We consider the following singularly perturbed Neumann problem (Lin-Ni-Takagi problem) ε∆u− u+ u = 0 , u > 0 in Ω, ∂u ∂ν = 0 on ∂Ω, where p > 2 and Ω is a smooth and bounded domain in R2. We construct a new class of solutions which consist of large number of spikes concentrating on a segment of the boundary which contains a strict local minimum point of the mean curvature function and has the s...
متن کاملOn the Problem of Stable Rational Interpolation
Aspects of the stability issue in connection with rational interpolation are investigated. In particular, it is shown that unconstrained interpolation of a given set of points together with an associated mirror-image set of points yields a one-parameter family of stable interpolating functions. As an application, it is also shown that if a certain number of Markov parameters are given, by appro...
متن کاملOn a Geometrical Interpolation Problem
Given a finite set of points A in R and a geometrical pattern Φ we define a type of distance between A and Φ and study how to find a pattern Φ among a parametrized family of geometrical objects such that such a distance is minimum. Mathematics Subject Classification: 41A29
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2007
ISSN: 0024-3795
DOI: 10.1016/j.laa.2007.02.020