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Journal articles on the topic 'Nevanlinna Problem'

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Published: 6 September 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

Thin, Nguyen Van, Ha Tran Phuong, and Leuanglith Vilaisavanh. "A uniqueness problem for entire functions related to Brück’s conjecture." Mathematica Slovaca 68, no. 4 (August 28, 2018): 823–36. http://dx.doi.org/10.1515/ms-2017-0148.

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Abstract In this paper, we prove a normal criteria for family of meromorphic functions. As an application of that result, we establish a uniqueness theorem for entire function concerning a conjecture of R. Brück. The above uniqueness theorem is an improvement of a problem studied by L. Z. Yang et al. [14]. However, our method differs the method of L. Z. Yang et al. [14]. We mainly use normal family theory and combine it with Nevanlinna theory instead of using only the Nevanlinna theory as in [14].
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8

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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9

Takahashi, Sechiko. "A sufficient condition for Nevanlinna parametrization and an extension of Heins theorem." Nagoya Mathematical Journal 153 (1999): 87–100. http://dx.doi.org/10.1017/s0027763000006905.

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AbstractAn extended interpolation problem on a Riemann surface is formulated in terms of local rings and ideals. A sufficient condition for Nevanlinna parametrization is obtained. By means of this, Heins theorem on Pick-Nevanlinna interpolation in doubly connected domains is generalized to extended interpolation.
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10

Takahashi, Sechiko. "Nevanlinna parametrizations for the extended interpolation problem." Pacific Journal of Mathematics 146, no. 1 (November 1, 1990): 115–29. http://dx.doi.org/10.2140/pjm.1990.146.115.

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11

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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12

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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13

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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14

Dyukarev, Yu M. "Nevanlinna–Pick Problem for Stieltjes Matrix Functions." Ukrainian Mathematical Journal 56, no. 3 (March 2004): 446–65. http://dx.doi.org/10.1023/b:ukma.0000045689.16180.31.

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15

Kosiński, Łukasz, and Włodzimierz Zwonek. "Nevanlinna-Pick interpolation problem in the ball." Transactions of the American Mathematical Society 370, no. 6 (November 14, 2017): 3931–47. http://dx.doi.org/10.1090/tran/7063.

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16

Li, Kin Y. "Nevanlinna-Pick problem on reproducing kernel spaces." 1 13 (2018): 33–40. http://dx.doi.org/10.12988/ijcms.2018.71240.

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17

Agler, J., and N. J. Young. "The two-point spectral Nevanlinna-Pick problem." Integral Equations and Operator Theory 37, no. 4 (December 2000): 375–85. http://dx.doi.org/10.1007/bf01192826.

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18

Bultheel, Adhemar, and Andreas Lasarow. "SCHUR–NEVANLINNA SEQUENCES OF RATIONAL FUNCTIONS." Proceedings of the Edinburgh Mathematical Society 50, no. 3 (October 2007): 571–96. http://dx.doi.org/10.1017/s0013091504001063.

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AbstractWe study certain sequences of rational functions with poles outside the unit circle. Such kinds of sequences are recursively constructed based on sequences of complex numbers with norm less than one. In fact, such sequences are closely related to the Schur–Nevanlinna algorithm for Schur functions on the one hand, and to orthogonal rational functions on the unit circle on the other. We shall see that rational functions belonging to a Schur–Nevanlinna sequence can be used to parametrize the set of all solutions of an interpolation problem of Nevanlinna–Pick type for Schur functions.
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19

Cherry, William, and Zhuan Ye. "Non-Archimedean Nevanlinna theory in several variables and the non-Archimedean Nevanlinna inverse problem." Transactions of the American Mathematical Society 349, no. 12 (1997): 5043–71. http://dx.doi.org/10.1090/s0002-9947-97-01874-6.

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20

Lopez-Rodriguez, Pedro. "The Nevanlinna parametrization for a matrix moment problem." MATHEMATICA SCANDINAVICA 89, no. 2 (December 1, 2001): 245. http://dx.doi.org/10.7146/math.scand.a-14340.

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We obtain the Nevanlinna parametrization for an indeterminate matrix moment problem, giving a homeomorphism between the set $V$ of solutions to the matrix moment problem and the set $\mathcal V$ of analytic matrix functions in the upper half plane such that $V(\lambda )^*V(\lambda )\le I$. We characterize the N-extremal matrices of measures (those for which the space of matrix polynomials is dense in their $L^2$-space) as those whose corresponding matrix function $V(\lambda )$ is a constant unitary matrix.
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21

Kosiński, Łukasz. "Three-point Nevanlinna–Pick problem in the polydisc." Proceedings of the London Mathematical Society 111, no. 4 (October 2015): 887–910. http://dx.doi.org/10.1112/plms/pdv045.

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22

Volkmann, Lutz. "A Remark on a Problem of Rolf Nevanlinna." Complex Variables, Theory and Application: An International Journal 47, no. 8 (August 2002): 727–29. http://dx.doi.org/10.1080/02781070290016412.

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23

COSTARA, CONSTANTIN. "THE $2\times 2$ SPECTRAL NEVANLINNA–PICK PROBLEM." Journal of the London Mathematical Society 71, no. 03 (May 24, 2005): 684–702. http://dx.doi.org/10.1112/s002461070500640x.

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24

Njåstad, Olav. "Nevanlinna matrices for the strong Stieltjes moment problem." Journal of Computational and Applied Mathematics 99, no. 1-2 (November 1998): 311–18. http://dx.doi.org/10.1016/s0377-0427(98)00165-4.

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25

Agler, Jim, and N. J. Young. "The two-by-two spectral Nevanlinna-Pick problem." Transactions of the American Mathematical Society 356, no. 2 (September 22, 2003): 573–85. http://dx.doi.org/10.1090/s0002-9947-03-03083-6.

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26

Bourdon, Paul S. "Rudin’s orthogonality problem and the Nevanlinna counting function." Proceedings of the American Mathematical Society 125, no. 4 (1997): 1187–92. http://dx.doi.org/10.1090/s0002-9939-97-03694-0.

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27

Njåstad, O. "Nevanlinna Matrices for the Strong Hamburger Moment Problem." Rocky Mountain Journal of Mathematics 33, no. 2 (June 2003): 475–88. http://dx.doi.org/10.1216/rmjm/1181069963.

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28

Njåstad, Olav. "Analytic functions associated with strong Hamburger moment problems." Proceedings of the Edinburgh Mathematical Society 52, no. 1 (February 2009): 181–87. http://dx.doi.org/10.1017/s0013091505001446.

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29

Zheleznyak, Аlexander V. "Multiplicative property of series used in the Nevanlinna-Pick problem." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 9, no. 1 (2022): 37–45. http://dx.doi.org/10.21638/spbu01.2022.104.

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In the paper we obtained substantially new sufficient condition for negativity of coefficients of power series inverse to series with positive ones. It has been proved that element-wise product of power series retains this property. In particular, it gives rise to generalization of the classical Hardy theorem about power series. These results are generalized for cases of series with multiple variables. Such results are useful in Nevanlinna – Pick theory. For example, if function k(x, y) can be represented as power series Pn≥0 an(x¯y)n, an > 0, and reciprocal function 1/k(x, y) can be represented as power series Pn≥0 bn(x¯y)n such that bn < 0, n > 0, then k(x, y) is a reproducing kernel function for some Hilbert space of analytic functions in the unit disc D with Nevanlinna – Pick property. The reproducing kernel 1/(1 − x¯y) of the classical Hardy space H2(D) is a prime example for our theorems.
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30

Agler, Jim, and John E. MCarthy. "Nevanlinna-Pick interpolation on the bidisk." Journal für die reine und angewandte Mathematik (Crelles Journal) 1999, no. 506 (January 15, 1999): 191–204. http://dx.doi.org/10.1515/crll.1999.506.191.

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Abstract We solve the matrix-valued Nevanlinna-Pick problem in the space of bounded analytic functions on the bidisk, and give a description of all the interpolating functions. We also prove the Toeplitz-corona theorem on the bidisk.
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31

Ozawa, Mitsuru. "A method to a problem of R. Nevanlinna. I." Kodai Mathematical Journal 8, no. 1 (1985): 14–24. http://dx.doi.org/10.2996/kmj/1138036993.

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32

Ozawa, Mitsuru. "A method to a problem of R. Nevanlinna. II." Kodai Mathematical Journal 8, no. 1 (1985): 25–32. http://dx.doi.org/10.2996/kmj/1138036994.

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33

Saitoh, Saburou. "A counter example in the Pick-Nevanlinna interpolation problem." Archiv der Mathematik 51, no. 2 (August 1988): 164–65. http://dx.doi.org/10.1007/bf01206474.

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34

Luxemburg, Leon A., and Philip R. Brown. "The scalar Nevanlinna–Pick interpolation problem with boundary conditions." Journal of Computational and Applied Mathematics 235, no. 8 (February 2011): 2615–25. http://dx.doi.org/10.1016/j.cam.2010.11.013.

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35

Baribeau, Line, Patrice Rivard, and Elias Wegert. "On Hyperbolic Divided Differences and the Nevanlinna-Pick Problem." Computational Methods and Function Theory 9, no. 2 (December 18, 2008): 391–405. http://dx.doi.org/10.1007/bf03321735.

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36

Zagorodnyuk, S. M. "Nevanlinna formula for the truncated matrix trigonometric moment problem." Ukrainian Mathematical Journal 64, no. 8 (January 2013): 1199–214. http://dx.doi.org/10.1007/s11253-013-0710-0.

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37

Oloomi, H. M. "Nevanlinna-Pick interpolation problem for two frequency scale systems." IEEE Transactions on Automatic Control 40, no. 1 (1995): 169–73. http://dx.doi.org/10.1109/9.362876.

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38

Буслаев, Виктор Иванович, and Viktor Ivanovich Buslaev. "On the solvability of the Nevanlinna-Pik interpolation problem." Математический сборник 214, no. 8 (2023): 18–52. http://dx.doi.org/10.4213/sm9826.

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В статье доказывается теорема о разрешимости интерполяционной проблемы Неванлинны-Пика, крайними случаями которой с одной стороны являются критерии Каратеодори и Шура (если все точки интерполяции совпадают между собой), а с другой - теорема Крейна-Рехтман (если все точки интерполяции попарно различны). Библиография: 19 названий.
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39

Tran Duc, Anh. "A NOTE ON S. TAKAHASHI’S ARTICLE." Journal of Science Natural Science 67, no. 3 (October 2022): 10–16. http://dx.doi.org/10.18173/2354-1059.2022-0036.

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40

Oanh, Bui Thi Kieu, and Ngo Thi Thu Thuy. "Uniqueness of Differential Polynomials of Meromorphic Functions Sharing a Small Function Without Counting Multiplicity." Fasciculi Mathematici 57, no. 1 (December 1, 2016): 121–35. http://dx.doi.org/10.1515/fascmath-2016-0020.

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Abstract The paper concerns interesting problems related to the field of Complex Analysis, in particular Nevanlinna theory of meromorphic functions. The author have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a small function without counting multiplicity. The results of this paper are extension of some problems studied by K. Boussaf et. al. in [2] and generalization of some results of S.S. Bhoosnurmath et. al. in [4].
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41

Zhang, Ke Yu. "Uniqueness of Q-Difference Polynomials of Meromorphic Functions." Advanced Materials Research 756-759 (September 2013): 2948–51. http://dx.doi.org/10.4028/www.scientific.net/amr.756-759.2948.

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In this paper, Applying the theory of Nevanlinna, we investigated uniqueness problem of difference polynomial of meromorphic functions and obtained uniqueness theorems of meromorphic functions , which Extended and improved the results of literature [5].
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42

Tolokonnikov, V. "Extremal functions of the Nevanlinna-Pick problem and Douglas algebras." Studia Mathematica 105, no. 2 (1993): 151–58. http://dx.doi.org/10.4064/sm-105-2-151-158.

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43

Chandel, Vikramjeet Singh. "The three-point Pick–Nevanlinna interpolation problem on the polydisc." Complex Variables and Elliptic Equations 63, no. 9 (September 8, 2017): 1341–52. http://dx.doi.org/10.1080/17476933.2017.1370461.

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44

Ball, Joseph A., Vladimir Bolotnikov, and Sanne ter Horst. "A constrained Nevanlinna-Pick interpolation problem for matrix-valued functions." Indiana University Mathematics Journal 59, no. 1 (2010): 15–52. http://dx.doi.org/10.1512/iumj.2010.59.3776.

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45

Baribeau, Line, and Adama S. Kamara. "A Refined Schwarz Lemma for the Spectral Nevanlinna-Pick Problem." Complex Analysis and Operator Theory 8, no. 2 (May 16, 2013): 529–36. http://dx.doi.org/10.1007/s11785-013-0306-6.

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46

Boyko, Olga, Olga Martinyuk, and Vyacheslav Pivovarchik. "Higher order Nevanlinna functions and the inverse three spectra problem." Opuscula Mathematica 36, no. 3 (2016): 301. http://dx.doi.org/10.7494/opmath.2016.36.3.301.

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47

Alpay, D., V. Bolotnikov, and A. Dijksma. "On the Nevanlinna-Pick interpolation problem for generalized stieltjes functions." Integral Equations and Operator Theory 30, no. 4 (December 1998): 379–408. http://dx.doi.org/10.1007/bf01257874.

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48

Shamoyan, R., and O. Mihi´c. "О некоторых новых теоремах в классах типа Неванлинны в единичном круге." Вестник КРАУНЦ. Физико-математические науки, no. 1 (April 17, 2023): 150–63. http://dx.doi.org/10.26117/2079-6641-2023-42-1-150-163.

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The study of various infinite products in various spaces of analytic functions in the unit disk is a well known and well studied problem of complex function theory in the unit disk. The goal of our paper is to study so-called Blashcke type products in new large, general analytic area Nevanlinna spaces in the unit disk.A new approach is suggested in this paper, namely we prove, use and apply various new embedding theorems which relate new general, large analytic area Nevanlinna spaces with less general well-studied and wellknown such type analytic spaces in the unit disk. Our theorems can be applied or can be used even in more general situation, when we consider large, general analytic area Nevanlinna spaces not in the unit disk, but in the circular ring.In our paper, using same approach new parametric representations of mentioned large, general analytic area Nevanlinna spaces are presented. These results also can be applied or used in the future to obtain more general theorems on parametric representations of mentioned large,general area Nevanlinna type spaces not in the unit disk, but in more general circular domains. Общая задача о принадлежности тех или иных бесконечных произведений тем или иным аналитическим классам функций хорошо известна в литературе. Цель исследования, в частности, рассмотреть и изучить вопрос о принадлежности бесконечных произведений типа Бляшке к общим новым широким классам типа Неванлинны в единичном круге. Авторы для этого применяют новый метод, а именно доказываются и приводятся в статье различные новые теоремы вложения,связывающие новые общие классы типа Неванлинны с уже хорошо изученными и известными менее общими классами типа Неванлинны в единичном круге. Результаты статьи могут быть обобщены или использованы в более общем случае, когда рассматриваются общие, широкие классы Неванлинны в круговом кольце. В статье тем же методом также получены новые параметрические представления указанных широких классов типа Неванлинны в единичном круге. Вывод: эти результаты также могут быть использованы для получения новых параметрических представлений общих классов типа Неванлинны в круговом кольце.
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49

Zheleznyak, A. V. "Multiplicative Property of the Series Used in the Nevanlinna–Pick Problem." Vestnik St. Petersburg University, Mathematics 55, no. 1 (March 2022): 27–33. http://dx.doi.org/10.1134/s1063454122010162.

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50

Rapisarda, Paolo, and Jan C. Willems. "The subspace Nevanlinna interpolation problem and the most powerful unfalsified model." Systems & Control Letters 32, no. 5 (December 1997): 291–300. http://dx.doi.org/10.1016/s0167-6911(97)00085-6.

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