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Academic literature on the topic 'Nevanlinna-Pick problem'

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Published: 6 September 2023

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Journal articles on the topic "Nevanlinna-Pick problem"

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Dyukarev, Yu M. "Degenerate Nevanlinna-Pick problem." Ukrainian Mathematical Journal 57, no. 10 (October 2005): 1559–70. http://dx.doi.org/10.1007/s11253-006-0014-8.

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El-Sabbagh, A. A. "On the solution of Nevanlinna Pick problem with selfadjoint extensions of symmetric linear relations in Hilbert space." International Journal of Mathematics and Mathematical Sciences 20, no. 3 (1997): 457–64. http://dx.doi.org/10.1155/s0161171297000628.

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The representation of Nevanlinna Pick Problem is well known, see [7], [8] and [11]. The aim of this paper is to find the necessary and sufficient condition for the solution of Nevanlinna Pick Problem and to show that there is a one-to-one correspondence between the solutions of the Nevanlinna Pick Problem and the minimal selfadjoint extensions of symmetric linear relation in Hilbert space. Finally, we define the resolvent matrix which gives the solutions of the Nevanlinna Pick Problem.
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Fisher, Stephen D., and Dmitry Khavinson. "Extreme Pick-Nevanlinna Interpolants." Canadian Journal of Mathematics 51, no. 5 (October 1, 1999): 977–95. http://dx.doi.org/10.4153/cjm-1999-043-5.

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AbstractFollowing the investigations of B. Abrahamse [1], F. Forelli [11], M. Heins [14] and others, we continue the study of the Pick-Nevanlinna interpolation problem inmultiply-connected planar domains. One major focus is on the problem of characterizing the extreme points of the convex set of interpolants of a fixed data set. Several other related problems are discussed.
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Costara, Constantin. "On the spectral Nevanlinna–Pick problem." Studia Mathematica 170, no. 1 (2005): 23–55. http://dx.doi.org/10.4064/sm170-1-2.

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Davidson, Kenneth R., Vern I. Paulsen, Mrinal Raghupathi, and Dinesh Singh. "A constrained Nevanlinna-Pick interpolation problem." Indiana University Mathematics Journal 58, no. 2 (2009): 709–32. http://dx.doi.org/10.1512/iumj.2009.58.3486.

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Hartz, Michael. "On the Isomorphism Problem for Multiplier Algebras of Nevanlinna-Pick Spaces." Canadian Journal of Mathematics 69, no. 1 (February 1, 2017): 54–106. http://dx.doi.org/10.4153/cjm-2015-050-6.

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AbstractWe continue the investigation of the isomorphism problem for multiplier algebras of reproducing kernel Hilbert spaces with the complete Nevanlinna-Pick property. In contrast to previous work in this area, we do not study these spaces by identifying them with the restrictions of a universal space, namely theDrury-Arveson space. Instead, we work directly with theHilbert spaces and their reproducing kernels. In particular, we show that two multiplier algebras of Nevanlinna-Pick spaces on the same set are equal if and only if the Hilbert spaces are equal. Most of the article is devoted to the study of a special class of complete Nevanlinna-Pick spaces on homogeneous varieties. We provide a complete answer to the question of when two multiplier algebras of spaces of this type are algebraically or isometrically isomorphic.This generalizes results of Davidson, Ramsey,Shalit, and the author.
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Yücesoy, Veysel, and Hitay Özbay. "On the real, rational, bounded, unit interpolation problem in ℋ∞ and its applications to strong stabilization." Transactions of the Institute of Measurement and Control 41, no. 2 (April 23, 2018): 476–83. http://dx.doi.org/10.1177/0142331218759598.

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One of the most challenging problems in feedback control is strong stabilization, i.e. stabilization by a stable controller. This problem has been shown to be equivalent to finding a finite dimensional, real, rational and bounded unit in [Formula: see text] satisfying certain interpolation conditions. The problem is transformed into a classical Nevanlinna–Pick interpolation problem by using a predetermined structure for the unit interpolating function and analysed through the associated Pick matrix. Sufficient conditions for the existence of the bounded unit interpolating function are derived. Based on these conditions, an algorithm is proposed to compute the unit interpolating function through an optimal solution to the Nevanlinna–Pick problem. The conservatism caused by the sufficient conditions is illustrated through strong stabilization examples taken from the literature.
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Stray, A. "Interpolating sequences and the Nevanlinna Pick problem." Publicacions Matemàtiques 35 (July 1, 1991): 507–16. http://dx.doi.org/10.5565/publmat_35291_14.

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Ionescu, A. "On the Operator-Valued Nevanlinna-Pick Problem." Zeitschrift für Analysis und ihre Anwendungen 14, no. 3 (1995): 431–39. http://dx.doi.org/10.4171/zaa/632.

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Derkach, V. A. "On Schur–Nevanlinna–Pick Indefinite Interpolation Problem." Ukrainian Mathematical Journal 55, no. 10 (October 2003): 1567–87. http://dx.doi.org/10.1023/b:ukma.0000022069.69507.bc.

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Dissertations / Theses on the topic "Nevanlinna-Pick problem"

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Fang, Quanlei. "Multivariable Interpolation Problems." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/28311.

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In this dissertation, we solve multivariable Nevanlinna-Pick type interpolation problems. Particularly, we consider the left tangential interpolation problems on the commutative or noncommutative unit ball. For the commutative setting, we discuss left-tangential operator-argument interpolation problems for Schur-class multipliers on the Drury-Arveson space and for the noncommutative setting, we discuss interpolation problems for Schur-class multipliers on Fock space. We apply the Krein-space geometry approach (also known as the Grassmannian Approach). To implement this approach J-versions of Beurling-Lax representers for shift-invariant subspaces are required. Here we obtain these J-Beurling-Lax theorems by the state-space method for both settings. We see that the Krein-space geometry method is particularly simple in solving the interpolation problems when the Beurling-Lax representer is bounded. The Potapov approach applies equally well whether the representer is bounded or not.
Ph. D.
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Rivard, Patrice. "Un lemme de Schwartz-Pick à points multiples." Master's thesis, Université Laval, 2007. http://hdl.handle.net/20.500.11794/19410.

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Beaulieu, Marie-Ailan. "Problèmes de Schwarz-Pick sur le bidisque symétrisé." Master's thesis, Université Laval, 2015. http://hdl.handle.net/20.500.11794/26203.

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Tableau d’honneur de la Faculté des études supérieures et postdoctorales, 2015-2016
Les systèmes de Schwarz-Pick sont de puissants outils qui permettent d'enrichir l'étude de la géométrie des domaines de l'espace à plusieurs variables complexes. Plus particulièrement, les pseudodistances de Carathéodory et de Kobayashi forment respectivement le plus grand et le plus petit système. L'objet de cet ouvrage consiste à regrouper et synthétiser les recherches autour du calcul de ces pseudodistances sur le bidisque symétrisé. Il s'agit d'un domaine de l'espace à deux variables complexes qui possède une géométrie riche et qui joue un rôle clé dans la résolution du problème de Nevanlinna-Pick spectral. Sur le bidisque symétrisé, il est possible de calculer explicitement la pseudodistance de Carathéodory par le biais de la théorie des opérateurs. Le calcul de la pseudodistance de Kobayashi, se fera elle à travers un problème d'interpolation du disque unité avec des valeurs cibles dans le bidisque symétrisé, résolu à l'aide du théorème de Nevanlinna-Pick classique.
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Karlsson, Johan. "Inverse Problems in Analytic Interpolation for Robust Control and Spectral Estimation." Doctoral thesis, Stockholm : Matematik, Mathematics, Kungliga Tekniska högskolan, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-9248.

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Tseng, WanFang, and 曾婉芳. "Minimal Realization for Two-Point Spectral Nevanlinna-Pick Problem." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/67148190034034596953.

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碩士
東海大學
數學系
91
Abstract Consider symmetrized bidisc int and spectral Nevanlinna-Pick Interpolation non-flat problem on it as: is an analytic such that and then is an analytic function defined on into and exist A.B.C.D matrix such that is called a realization of . In this paper,we want to find the lower order of the realization. In fact , is a matrix. Change to become In other words keywords:symmetrizrd bidisc,spectral Nevanlinna-Pick problem realization, -extremal
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Lin, Chun-Ming, and 林俊銘. "Realization of Spectral Nevanlinna-Pick Interpolation Problem on Symmetrized Bidisc." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/40559244736778567050.

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碩士
東海大學
數學系
91
In this paper we discuss the two-point spectral Nevanlinna-Pick interpolation problem for 2 2 general case by using the previous results of T.D.Lin[13], C.T.Lin[8] and Yeh[9]: Given distinct ， ， ， ,find an analytic function such that and it's realization.
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Chandel, Vikramjeet Singh. "The Pick-Nevanlinna Interpolation Problem : Complex-analytic Methods in Special Domains." Thesis, 2017. http://etd.iisc.ernet.in/2005/3700.

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The Pick–Nevanlinna interpolation problem, in its fullest generality, is as follows: Given domains D1, D2 in complex Euclidean spaces, and a set f¹ zi; wiº : 1 i N g D1 D2, where zi are distinct and N 2 š+, N 2, find necessary and sufficient conditions for the existence of a holomorphic map F : D1 ! D2 such that F¹ziº = wi, 1 i N. When such a map F exists, we say that F is an interpolant of the data. Of course, this problem is intractable at the above level of generality. However, two special cases of the problem — which we shall study in this thesis — have been of lasting interest: Interpolation from the polydisc to the unit disc. This is the case D1 = „n and D2 = „, where „ denotes the open unit disc in the complex plane and n 2 š+. The problem itself originates with Georg Pick’s well-known theorem (independently discovered by Nevanlinna) for the case n = 1. Much later, Sarason gave another proof of Pick’s result using an operator-theoretic approach, which is very influential. Using this approach for n 2, Agler–McCarthy provided a solution to the problem with the restriction that the interpolant is in the Schur– Agler class. This is notable because, when n = 2, the latter result completely solves the problem for the case D1 = „2; D2 = „. However, Pick’s approach can also be effective for n 2. In this thesis, we give an alternative characterization for the existence of a 3-point interpolant based on Pick’s approach and involving the study of rational inner functions. Cole–Lewis–Wermer lifted Sarason’s approach to uniform algebras — leading to a char-acterization for the existence of an interpolant in terms of the positivity of a large, rather abstractly-defined family of N N matrices. McCullough later refined their result by identifying a smaller family of matrices. The second result of this thesis is in the same vein, namely: it provides a characterization of those data that admit a „n-to-„ interpolant in terms of the positivity of a family of N N matrices parametrized by a class of polynomials. Interpolation from the unit disc to the spectral unit ball. This is the case D1 = „ and D2 = n , where n denotes the set of all n n matrices with spectral radius less than 1. The interest in this arises from problems in Control Theory. Bercovici–Foias–Tannenbaum adapted Sarason’s methods to give a (somewhat hard-to-check) characterization for the existence of an interpolant under a very mild restriction. Later, Agler–Young established a relation between the interpolation problem in the spectral unit ball and that in the symmetrized polydisc — leading to a necessary condition for the existence of an interpolant. Bharali later provided a new inequivalent necessary condition for the existence of an interpolant for any n and N = 2. In this thesis, we shall present a necessary condition for the existence of an interpolant in the case when N = 3. This we shall achieve by adapting Pick’s approach and applying the aforementioned result of Bharali.
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Chen, Po-Jen, and 陳柏仁. "The Gamma(Γ)2-inner Solution of Three-point Spectral Nevanlinna-Pick Interpolation Problem:2x2case." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/16327064924593773842.

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碩士
東海大學
數學系
94
The spectral Nevanlinna-Pick interpolation theory is the main tool to setup the define theory for Mu-synthesis theory for robust controller design and is still under development. For 2x2 case only the solutions with 2 interpolating points is solved. In present thesis, we study how to construct the solutions corresponding to the 3 in-terpolating points with 3 cases on the symmetrized bidisc. Furthermore, the idea to solve interpolating points is also discussed.
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Rivard, Patrice. "Un lemme de Schwartz-Pick à points multiples /." 2007. http://www.theses.ulaval.ca/2007/24845/24845.pdf.

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Chen, Kuan-Lung, and 陳冠龍. "Existence and Characterization of Solutions to Polytope and Disk Perturbed H∞ Nevanlinna-Pick Interpolation Problems." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/32270199680868767878.

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碩士
國立海洋大學
電子工程學系
83
Based on the standard H∞ Nevanlinna-Pick Interpolation Theory and Kharitonov Theory, this thesis will derive a necessary and sufficient condition for the existence of solutions to the polytope and disk perturbed H∞ Nevanlinna-Pick interpolation problem. Under this condition, the general solutions to the perturbed H∞ Nevanlinna-Pick interpolation problem will be also characterized.
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Book chapters on the topic "Nevanlinna-Pick problem"

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Dijksma, Aad, and Heinz Langer. "Notes on a Nevanlinna-Pick interpolation problem for generalized Nevanlinna functions." In Topics in Interpolation Theory, 69–91. Basel: Birkhäuser Basel, 1997. http://dx.doi.org/10.1007/978-3-0348-8944-5_4.

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Ball, Joseph A., and D. William Luse. "Sensitivity Minimization as a Nevanlinna-Pick Interpolation Problem." In Modelling, Robustness and Sensitivity Reduction in Control Systems, 451–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-87516-8_26.

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Ball, Joseph A., and Vladimir Bolotnikov. "The Bitangential Matrix Nevanlinna–Pick Interpolation Problem Revisited." In Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations, 107–61. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-68849-7_5.

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Frazho, A. E., S. ter Horst, and M. A. Kaashoek. "All Solutions to an Operator Nevanlinna–Pick Interpolation Problem." In Operator Theory in Different Settings and Related Applications, 139–220. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-62527-0_5.

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Sarason, Donald. "Operator-Theoretic Aspects of the Nevanlinna-Pick Interpolation Problem." In Operators and Function Theory, 279–314. Dordrecht: Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5374-1_9.

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Bolotnikov, Vladimir. "The two-sided Nevanlinna-Pick problem in the Stieltjes class." In Contributions to Operator Theory and its Applications, 15–37. Basel: Birkhäuser Basel, 1993. http://dx.doi.org/10.1007/978-3-0348-8581-2_2.

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Langer, H., and H. Woracek. "Resolvents of symmetric sperators and the degenerated Nevanlinna-Pick problem." In Recent Progress in Operator Theory, 233–61. Basel: Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8793-9_13.

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Tannenbaum, Allen R. "Spectral Nevanlinna-Pick Interpolation." In Open Problems in Mathematical Systems and Control Theory, 217–20. London: Springer London, 1999. http://dx.doi.org/10.1007/978-1-4471-0807-8_41.

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Kheifets, A. Ya, and P. M. Yuditskii. "An Analysis and Extension of V.P. Potapov’s Approach to Interpolation Problems with Applications to the Generalized Bi-Tangential Schur-Nevanlinna-Pick Problem and J-Inner-Outer Factorization." In Matrix and Operator Valued Functions, 133–61. Basel: Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-8532-4_6.

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Hassi, Seppo, Henk De Snoo, and Harald Woracek. "Some interpolation problems of Nevanlinna-Pick type. The Kreĭn-Langer method." In Contributions to Operator Theory in Spaces with an Indefinite Metric, 201–16. Basel: Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8812-7_10.

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Conference papers on the topic "Nevanlinna-Pick problem"

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Yazici, Cuneyt, and Hulya Kodal Sevindir. "A correction for computing matrix-valued Nevanlinna-Pick interpolation problem." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4826042.

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