Relevant bibliographies by topics / Nevanlinna-Pick interpolation problems

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Nevanlinna-Pick interpolation problems'

Author: Grafiati
Published: 4 June 2021
Last updated: 9 February 2022

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Journal articles on the topic "Nevanlinna-Pick interpolation problems"

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Yücesoy, Veysel, та 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, № 2 (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.
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Ball, Joseph A., J. William Helton, and C. H. Sung. "Nonlinear solutions of Nevanlinna-Pick interpolation problems." Michigan Mathematical Journal 34, no. 3 (1987): 375–89. http://dx.doi.org/10.1307/mmj/1029003619.

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Fisher, Stephen D., and Dmitry Khavinson. "Extreme Pick-Nevanlinna Interpolants." Canadian Journal of Mathematics 51, no. 5 (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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Constantinescu, T., and J. L. Johnson. "A Note on Noncommutative Interpolation." Canadian Mathematical Bulletin 46, no. 1 (2003): 59–70. http://dx.doi.org/10.4153/cmb-2003-006-4.

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AbstractIn this paper we formulate and solve Nevanlinna-Pick and Carathéodory type problems for tensor algebras with data given on the N-dimensional operator unit ball of a Hilbert space. We develop an approach based on the displacement structure theory.
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Song, Yan-Ping, Hui-Feng Hao, Yong-Jian Hu, and Gong-Ning Chen. "Some Propositions on Generalized Nevanlinna Functions of the ClassNk." Advances in Mathematical Physics 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/605492.

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Some propositions on the generalized Nevanlinna functions are derived. We indicate mainly that (1) the negative inertia index of a Hermitian generalized Loewner matrix generated by a generalized Nevanlinna function in the classNκdoes not exceedκ. This leads to an equivalent definition of a generalized Nevanlinna function; (2) if a generalized Nevanlinna function in the classNκhas a uniform asymptotic expansion at a real pointαor at infinity, then the negative inertia index of the Hankel matrix constructed with the partial coefficients of that asymptotic expansion does not exceedκ. Also, an exp
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Gong-Ning Chen and Xiao-Qing Li. "The Nevanlinna-Pick interpolation problems and power moment problems for matrix-valued functions." Linear Algebra and its Applications 288 (February 1999): 123–48. http://dx.doi.org/10.1016/s0024-3795(98)10188-x.

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Heins, Maurice. "On an example of donald marshall concerning automorphic pick—nevanlinna interpolation problems." Complex Variables, Theory and Application: An International Journal 7, no. 1-3 (1986): 71–78. http://dx.doi.org/10.1080/17476938608814187.

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Wu, Huazhang. "On the multiple Nevanlinna–Pick interpolation problems in some matrix-valued function classes." Linear Algebra and its Applications 399 (April 2005): 71–90. http://dx.doi.org/10.1016/j.laa.2004.06.012.

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Ball, Joseph A., and Vladimir Bolotnikov. "Interpolation Problems for Schur Multipliers on the Drury-Arveson Space: from Nevanlinna-Pick to Abstract Interpolation Problem." Integral Equations and Operator Theory 62, no. 3 (2008): 301–49. http://dx.doi.org/10.1007/s00020-008-1626-1.

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Yung, Chee-Fai, Fang-Bo Yeh, Jyun-Tswun Lin, and Kuan-Lung Chen. "A NECESSARY AND SUFFICIENT CONDITION FOR THE SOLVABILITY OF PERTURBED NEVANLINNA-PICK INTERPOLATION PROBLEMS." Journal of the Chinese Institute of Engineers 20, no. 5 (1997): 579–84. http://dx.doi.org/10.1080/02533839.1997.9741864.

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Dissertations / Theses on the topic "Nevanlinna-Pick interpolation problems"

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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 B
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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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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<br>國立海洋大學<br>電子工程學系<br>83<br>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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Zhan, Xuzhou. "On matrix generalization of Hurwitz polynomials." Doctoral thesis, 2017. https://ul.qucosa.de/id/qucosa%3A16415.

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This thesis focuses on matrix generalizations of Hurwitz polynomials. A real polynomial with all its roots in the open left half plane of the complex plane is called a Hurwitz polynomial. The study of these Hurwitz polynomials has a long and abundant history, which is associated with the names of Hermite, Routh, Hurwitz, Liénard, Chipart, Wall, Gantmacher et al. The direct matricial generalization of Hurwitz polynomials is naturally defined as follows: A p by p matrix polynomial F is called a Hurwitz matrix polynomial if the determinant of F is a Hurwitz polynomial. Recently, Choque Rivero fo
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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<br>東海大學<br>數學系<br>91<br>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: Interp
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Chen, Po-Jen, та 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<br>東海大學<br>數學系<br>94<br>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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Book chapters on the topic "Nevanlinna-Pick interpolation problems"

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

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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. Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8812-7_10.

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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. Birkhäuser Basel, 1997. http://dx.doi.org/10.1007/978-3-0348-8944-5_4.

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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. Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-8532-4_6.

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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. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-68849-7_5.

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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. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-87516-8_26.

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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. 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. Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5374-1_9.

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"Hilbert function spaces and Nevanlinna-Pick kernels." In Function Theory: Interpolation and Corona Problems. American Mathematical Society, 2009. http://dx.doi.org/10.1090/fim/025/05.

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"The Nevanlinna-Pick Problem". У 𝐽 Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces and Interpolation. American Mathematical Society, 1989. http://dx.doi.org/10.1090/cbms/071/06.

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Conference papers on the topic "Nevanlinna-Pick interpolation problems"

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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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