Convex cones of generalized positive rational functions and the Nevanlinna–Pick interpolation
نویسندگان
چکیده
منابع مشابه
Extremal Positive Splines with Applications to Interpolation and Approximation by Generalized Convex Functions
F(s, t) = wn(s)w0(t) dtiw^) dt2w2(t2) • • • </*„__!*„_!(*„_!). Jt Jtl Jtn-2 A fundamental solution for L is given by G(s, t) = F(s, t) for s ^ t, G(s, t) = 0 for s < t. A fundamental solution for L* is GJs, i) = G(t, s). To avoid cumbersome formulations results are stated for n ^ 2 (in which case G is continuous), unless indicated otherwise. By SR(T) we mean the collection of Radon measures on ...
متن کاملThe positive real lemma and construction of all realizations of generalized positive rational functions
We here extend the well known Positive Real Lemma (also known as the Kalman-Yakubovich-Popov Lemma) to complex matrix-valued generalized positive rational function, when non-minimal realizations are considered. All state space realizations are partitioned into subsets, each is identified with a set of matrices satisfying the same Lyapunov inclusion. Thus, each subset forms a convex invertible c...
متن کاملGeneralized Hermite Interpolation via Matrix-valued Conditionally Positive Definite Functions
In this paper, we consider a broad class of interpolation problems, for both scalarand vector-valued multivariate functions subject to linear side conditions, such as being divergence-free, where the data are generated via integration against compactly supported distributions. We show that, by using certain families of matrix-valued conditionally positive definite functions, such interpolation ...
متن کاملBornological Completion of Locally Convex Cones
In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.
متن کاملGeneralized convex functions and generalized di¤erentials
We study some classes of generalized convex functions, using a generalized di¤erential approach. By this we mean a set-valued mapping which stands either for a derivative, a subdi¤erential or a pseudodi¤erential in the sense of Jeyakumar and Luc. We establish some links between the corresponding classes of pseudoconvex, quasiconvex and another class of generalized convex functions we introduced...
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: 2013
ISSN: 0024-3795
DOI: 10.1016/j.laa.2012.01.023