The Schur algorithm and reproducing kernel Hilbert spaces in the ball

Alpay, D
Bolotnikov, V
Kaptanoglu, HT
Using reproducing kernel Hilbert spaces methods we develop a Schur-type algorithm for a subclass of the functions analytic and contractive in the ball. We also consider the Nevanlinna-Pick interpolation problem in that class. (C) 2002 Elsevier Science Inc. All rights reserved.


Quivers of finite mutation type and skew-symmetric matrices
Seven, Ahmet İrfan (Elsevier BV, 2010-11-01)
Quivers of finite mutation type are certain directed graphs that first arised in Fomin-Zelevinsky's theory of cluster algebras. It has been observed that these quivers are also closely related with different areas of mathematics. In fact, main examples of finite mutation type quivers are the quivers associated with triangulations of surfaces. In this paper, we study structural properties of finite mutation type quivers in relation with the corresponding skew-symmetric matrices. We obtain a characterization ...
Contour approximation of data: A duality theory
İyigün, Cem (Elsevier BV, 2009-05-01)
Given a dataset D partitioned in clusters, the joint distance function (JDF)J(x) at any point x is the harmonic mean of the distances between x and the cluster centers. The JDF is a continuous function, capturing the data points in its lower level sets (a property called contour approximation), and is a useful concept in probabilistic clustering and data analysis.
On q-ary plateaued functions over F-q and their explicit characterizations
Mesnager, Sihem; Özbudak, Ferruh; Sinak, Ahmet; Cohen, Gerard (Elsevier BV, 2019-08-01)
Plateaued and bent functions play a significant role in cryptography, sequence theory, coding theory and combinatorics. In 1997, Coulter and Matthews redefined bent functions over any finite field F-q where q is a prime power, and established their properties. The objective of this work is to redefine the notion of plateaued functions over F-q, and to present several explicit characterizations of those functions. We first give, over F-q, the notion of q-ary plateaued functions, which relies on the concept o...
The classical involution theorem for groups of finite Morley rank
Berkman, A (Elsevier BV, 2001-09-15)
This paper gives a partial answer to the Cherlin-Zil'ber Conjecture, which states that every infinite simple group of finite Morley rank is isomorphic to an algebraic group over an algebraically closed field. The classification of the generic case of tame groups of odd type follows from the main result of this work, which is an analogue of Aschbacher's Classical Involution Theorem for finite simple groups. (C) 2001 Academic Press.
Mutation classes of finite type cluster algebras with principal coefficients
Seven, Ahmet İrfan (Elsevier BV, 2013-06-15)
Cluster algebras of finite type is a fundamental class of algebras whose classification is identical to the famous Cartan Killing classification. More recently, Fomin and Zelevinslcy introduced another central notion of cluster algebras with principal coefficients. These algebras are determined combinatorially by mutation classes of certain rectangular matrices. It was conjectured, by Fomin and Zelevinsky, that finite type cluster algebras with principal coefficients are characterized by the mutation classe...
Citation Formats
D. Alpay, V. Bolotnikov, and H. Kaptanoglu, “The Schur algorithm and reproducing kernel Hilbert spaces in the ball,” LINEAR ALGEBRA AND ITS APPLICATIONS, pp. 163–186, 2002, Accessed: 00, 2020. [Online]. Available: