Positive and Generalized Positive Real Lemma for Slice Hyperholomorphic Functions

被引：0
作者：
Daniel Alpay
Fabrizio Colombo
Izchak Lewkowicz
Irene Sabadini
机构：
[1] Chapman University,Faculty of Mathematics, Physics, and Computation, Schmid College of Science and Technology
[2] Politecnico di Milano,Dipartimento di Matematica
[3] Ben-Gurion University of the Negev,Department of Electrical Engineering
来源：
Integral Equations and Operator Theory | 2019年 / 91卷
关键词：
Positive real functions; Kalman–Yakubovich–Popov lemma; Slice hyperholomorphic functions; Unit ball; Half space; Negative squares; Primary 30C40; Secondary 30G35; 93B15;
D O I：
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摘要：
In this paper we prove a quaternionic positive real lemma as well as its generalized version, in case the associated kernel has negative squares for slice hyperholomorphic functions. We consider the case of functions with positive real part in the half space of quaternions with positive real part, as well as the case of (generalized) Schur functions in the open unit ball.
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[1]  
Abu-Ghanem Kh(2018)Herglotz functions of several quaternionic variables J. Math. Anal. Appl. 466 169-182
[2]  
Alpay D(1991)Some remarks on reproducing kernel Krein spaces Rocky Mt. J. Math. 21 1189-1205
[3]  
Colombo F(1992)On linear combination of positive functions, associated reproducing kernel spaces and a nonhermitian Schur algorithm Arch. Math. (Basel) 58 174-182
[4]  
Lewkowicz I(2015)Self-mappings of the quaternionic unit ball: multiplier properties, Schwarz–Pick inequality, and Nevanlinna–Pick interpolation problem Indiana Univ. Math. J. 64 151-180
[5]  
Sabadini I(2015)An extension of Herglotz’s theorem to the quaternions J. Math. Anal. Appl. 421 754-778
[6]  
Alpay D(2015)Realizations of slice hyperholomorphic generalized contractive and positive functions Milan J. Math. 83 91-144
[7]  
Alpay D(2013)Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions J. Anal. Math. 121 87-125
[8]  
Alpay D(2003)Notes on interpolation in the generalized Schur class II. Nudel Trans. Am. Math. Soc. 355 813-836
[9]  
Bolotnikov V(2011)man’s problem. Syst. Control Lett. 60 985-993
[10]  
Colombo F(1968)The positive real lemma and construction of all realizations of generalized positive rational functions SIAM J. Control 6 615-624
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