Normes des extensions quaternionique d'opérateurs réels

We consider bounded linear operators defined on real normed spaces, and with range in quaternionic spaces. We study the norms of the quaternionic extensions of such operators. To cite this article: D. Alpay et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

The Schur Transformation for Generalized Nevanlinna Functions: Interpolation and Self-Adjoint Operator Realizations

The Schur transformation for generalized Nevanlinna functions has been defined and applied in [2]. In this paper we discuss its relation to a basic interpolation problem and study its effect on the minimal self-adjoint operator (or relation) realization of a generalized Nevanlinna function. D. Alpay acknowledges with thanks the Earl Katz family for endowing the chair which supported this research and the Netherlands Organization for Scientific Research, NWO (grant B 61-524). The research of A. Dijksma and H. Langer was partly supported by the Center for Advanced Studies in Mathematics, CASM, of the Department of Mathematics of Ben-Gurion University, that of H. Langer also by the Austrian Science Fund, Project P15540-N05. Received: September 25, 2006. Accepted: October 11, 2006.     

The Spectral Theorem for Unitary Operators Based on the S-Spectrum

The quaternionic spectral theorem has already been considered in the literature, see e.g. [22], [32], [33], however, except for the finite dimensional case in which the notion of spectrum is associated to an eigenvalue problem, see [21], it is not specified which notion of spectrum underlies the theorem.     

Mesoporous Manganese Oxide Catalyzed Aerobic Oxidative Coupling of Anilines To Aromatic Azo Compounds

Herein we introduce an environmentally friendly approach to the synthesis of symmetrical and asymmetrical aromatic azo compounds by using air as the sole oxidant under mild reaction conditions in the presence of cost‐effective and reusable mesoporous manganese oxide materials.     

On the Structure of the Taylor Series in Clifford and Quaternionic Analysis

The Fueter variables form a basis of the space of (quaternionic or Cliffordian) hyperholomorphic homogeneous polynomials of degree one, and their symmetrized products give the respective bases of spaces of hyperholomorphic homogeneous polynomials for any degree k. In the present paper we introduce new bases, i.e., new types of hyperholomorphic variables which lead to the Taylor-type series expansions reflecting the structure of the set of all (quaternionic or Cliffordian algebra-valued) hyperholomorphic functions.     

Schur Algorithm in The Class {\mathcal{SI}} of J-contractive Functions Intertwining Solutions of Linear Differential Equations

In the PhD thesis of the second author under the supervision of the third author was defined the class ${\mathcal{SI}}$ of J-contractive functions, depending on a parameter and arising as transfer functions of overdetermined conservative 2D systems invariant in one direction. In this paper we extend and solve in the class ${\mathcal{SI}}$ , a number of problems originally set for the class ${\mathcal{S}}$ of functions contractive in the open right-half plane, and unitary on the imaginary line with respect to some preassigned signature matrix J. The problems we consider include the Schur algorithm and the Nevanlinna–Pick interpolation problem. The arguments rely on a correspondence between elements in a given subclass of ${\mathcal{SI}}$ and elements in ${\mathcal{S}}$ . Another important tool in the arguments is a new result pertaining to the classical tangential Schur algorithm.     

Carathéodory-Fejér interpolation in locally convex topological vector spaces

We study Carathéodory-Herglotz functions whose values are continuous operators from a locally convex topological vector space which admits the factorization property into its conjugate dual space. We show how this case can be reduced to the case of functions whose values are bounded operators from a Hilbert space into itself.     

One-sided tangential interpolation for operator-valued Hardy functions on polydisks

All solutions of one-sided tangential interpolation problems with Hilbert norm constraints for operator-valued Hardy functions on the polydisk are described. The minimal norm solution is explicitly expressed in terms of the interpolation data.The research of this author is partially supported by NSF grant DMS 9800704, and by the Faculty Research Assignment grant from the College of William and Mary.