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61.
We study various aspects of Schur analysis in the slice hyperholomorphic setting. We present two sets of results: first, we give new results on the functional calculus for slice hyperholomorphic functions. In particular, we introduce and study some properties of the Riesz projectors. Then we prove a Beurling–Lax type theorem, the so-called structure theorem. A crucial fact which allows to prove our results is the fact that the right spectrum of a quaternionic linear operator and the point S-spectrum coincide. Finally, we study the Krein–Langer factorization for slice hyperholomorphic generalized Schur functions. Both the Beurling–Lax type theorem and the Krein–Langer factorization are far-reaching results which have not been proved in the quaternionic setting using notions of hyperholomorphy other than slice hyperholomorphy. 相似文献
62.
63.
Daniel Alpay Maria-Elena Luna-Elizarrarás Michael Shapiro 《Comptes Rendus Mathematique》2005,340(9):639-643
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). 相似文献
64.
Daniel Alpay Aad Dijksma Heinz Langer Yuri Shondin 《Complex Analysis and Operator Theory》2007,1(2):169-210
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. 相似文献
65.
66.
67.
Daniel Alpay Fabrizio Colombo David P. Kimsey Irene Sabadini 《Milan Journal of Mathematics》2016,84(1):41-61
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. 相似文献
68.
Mesoporous Manganese Oxide Catalyzed Aerobic Oxidative Coupling of Anilines To Aromatic Azo Compounds
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Dr. Vinit Sharma Prof. Nancy Ortins Savage Prof. S. Pamir Alpay Prof. Steven L. Suib 《Angewandte Chemie (International ed. in English)》2016,55(6):2171-2175
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. 相似文献
69.
Daniel Alpay Flor de María Correa-Romero María Elena Luna-Elizarrarás Michael Shapiro 《Integral Equations and Operator Theory》2011,71(3):311-326
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. 相似文献
70.
Daniel Alpay Andrey Melnikov Victor Vinnikov 《Integral Equations and Operator Theory》2012,74(3):313-344
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. 相似文献