Relevant bibliographies by topics / Symmetrized bidisk

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

Academic literature on the topic 'Symmetrized bidisk'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Symmetrized bidisk"

1

Bhattacharyya, Tirthankar, and Haripada Sau. "Interpolating sequences and the Toeplitz--Corona theorem on the symmetrized bidisk." Journal of Operator Theory 87, no. 1 (March 15, 2022): 435–59. http://dx.doi.org/10.7900/jot.2020oct07.2311.

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Bhattacharyya, Tirthankar, and Haripada Sau. "Holomorphic functions on the symmetrized bidisk – Realization, interpolation and extension." Journal of Functional Analysis 274, no. 2 (January 2018): 504–24. http://dx.doi.org/10.1016/j.jfa.2017.09.013.

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Agler, J., and N. J. Young. "Operators having the symmetrized bidisc as a spectral set." Proceedings of the Edinburgh Mathematical Society 43, no. 1 (February 2000): 195–210. http://dx.doi.org/10.1017/s0013091500020812.

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AbstractWe characterize those commuting pairs of operators on Hubert space that have the symmetrized bidisc as a spectral set in terms of the positivity of a hermitian operator pencil (without any assumption about the joint spectrum of the pair). Further equivalent conditions are that the pair has a normal dilation to the distinguished boundary of the symmetrized bidisc, and that the pair has the symmetrized bidisc as a complete spectral set. A consequence is that every contractive representation of the operator algebra A(Γ) of continuous functions on the symmetrized bidisc analytic in the interior is completely contractive. The proofs depend on a polynomial identity that is derived with the aid of a realization formula for doubly symmetric hereditary polynomials, which are positive on commuting pairs of contractions.
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Sarkar, Jaydeb. "Operator Theory on Symmetrized Bidisc." Indiana University Mathematics Journal 64, no. 3 (2015): 847–73. http://dx.doi.org/10.1512/iumj.2015.64.5541.

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Trybuła, Maria. "Invariant metrics on the symmetrized bidisc." Complex Variables and Elliptic Equations 60, no. 4 (August 28, 2014): 559–65. http://dx.doi.org/10.1080/17476933.2014.948543.

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COSTARA, C. "THE SYMMETRIZED BIDISC AND LEMPERT'S THEOREM." Bulletin of the London Mathematical Society 36, no. 05 (August 24, 2004): 656–62. http://dx.doi.org/10.1112/s0024609304003200.

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Pflug, Peter, and Włodzimierz Zwonek. "Exhausting domains of the symmetrized bidisc." Arkiv för Matematik 50, no. 2 (October 2012): 397–402. http://dx.doi.org/10.1007/s11512-011-0153-5.

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Bhattacharyya, Tirthankar, Anindya Biswas, and Anwoy Maitra. "On the geometry of the symmetrized bidisc." Indiana University Mathematics Journal 71, no. 2 (2022): 685–713. http://dx.doi.org/10.1512/iumj.2022.71.8896.

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Agler, Jim, Zinaida A. Lykova, and N. J. Young. "Extremal holomorphic maps and the symmetrized bidisc." Proceedings of the London Mathematical Society 106, no. 4 (October 26, 2012): 781–818. http://dx.doi.org/10.1112/plms/pds049.

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Agler, J., and N. J. Young. "A Schwarz Lemma for the Symmetrized Bidisc." Bulletin of the London Mathematical Society 33, no. 2 (March 2001): 175–86. http://dx.doi.org/10.1112/blms/33.2.175.

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Dissertations / Theses on the topic "Symmetrized bidisk"

1

Lin, Cheng-Tsai, and 林成財. "Schwarz Lemma on Symmetrized Bidisc." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/05462082649779495998.

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碩士
東海大學
數學系
89
Let $\Gamma$ denote the set of symmetrized bidisc. In this thesis we discuss the Schwarz lemma on $\Gamma$ also known as the special flat problem on $\Gamma$ as: Given $\alpha_{2}\in\mathbb{D},~\alpha_{2}\neq0~$ and $(s_{2},p_{2})\in\Gamma$, find an analytic function $\varphi:\mathbb{D}\rightarrow\Gamma$with $\varphi(\lambda)=(s(\lambda),p(\lambda))$ satisfies $$\varphi(0)=(0,0),~\varphi(\alpha_{2})=(s_{2},p_{2})$$ Based on the equality of Carath\'odory and Kobayashi distances, and the Schur's theorem, we construct an analytic function $\varphi$ to solve this problem. Keywords: Spectral Nevanlinna-Pick interpolation, Poincar\'{e} distance, Carath\'odory distance, Kobayashi distance, Symmetrized bidisc, Schwarz lemma.
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Lin, Tien-De, and 林天得. "Spectral Nevanlinna-Pick Interpolation On Symmetrized Bidisc." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/94495204389019542431.

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Abstract:
碩士
東海大學
數學系
89
Consider symmetrized bidisc $\Gamma_{2}$:% $$\Gamma_{2}\triangleq \{(s,p):\lambda^{2}-s\lambda+p=0,~\lambda \in \mathbb{C},~|\lambda|\leq1\}$$% and spectral Nevanlinna-Pick Interpolation non-flat problem on it as:\\ % Given $\alpha_{1},~\alpha_{2} \in \mathbb{D},~(s_{1},0),~(s_{2},0) % \in {\rm Int}~\Gamma_{2} $,% $\varphi : \mathbb{D} \longrightarrow {\rm Int}~\Gamma_{2}$,is analytic,% ~such that~$\varphi(\alpha_{1}) = (s_{1},0)$，$\varphi(\alpha_{2}) = (s_{2},~0)$,% ~by the equality of Carath$\acute{e}$odory and Kobayashi distances,% ~and Schur theorem, ~we can find $\varphi$ that we want.
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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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Abstract:
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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Sau, Haripada. "Operator Theory on Symmetrized Bidisc and Tetrablock-some Explicit Constructions." Thesis, 2015. http://etd.iisc.ernet.in/2005/3887.

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A pair of commuting bounded operators (S; P ) acting on a Hilbert space, is called a -contraction, if it has the symmetrised bides = f(z1 + z2; z1z2) : jz1j 1; jz2j 1g C2 as a spectral set. For every -contraction (S; P ), the operator equation S S P = DP F DP has a unique solution F 2 B(DP ) with numerical radius, denoted by w(F ), no greater than one, where DP is the positive square root of (I P P ) and DP = RanDP . This unique operator is called the fundamental operator of (S; P ). This thesis constructs an explicit normal boundary dilation for -contractions. A triple of commuting bounded operators (A; B; P ) acting on a Hilbert space with the tetra block E = f(a11; a22; detA) : A = a11 a12 with kAk 1g C 3 a21 a22 as a spectral set, is called a tetra block contraction. Every tetra block contraction possesses two fundamental operators and these are the unique solutions of A B P = DP F1DP ; and B A P = DP F2DP : Moreover, w(F1) and w(F2) are no greater than one. This thesis also constructs an explicit normal boundary dilation for tetra block contractions. In these constructions, the fundamental operators play a pivotal role. Both the dilations in the symmetrised bidisc and in the tetra block are proved to be minimal. But unlike the one variable case, uniqueness of minimal dilations fails in general in several variables, e.g., Ando's dilation is not unique, see [44]. However, we show that the dilations are unique under a certain natural condition. In view of the abundance of operators and their complicated structure, a basic problem in operator theory is to find nice functional models and complete sets of unitary invariants. We develop a functional model theory for a special class of triples of commuting bounded operators associated with the tetra block. We also find a set of complete unitary invariants for this special class. Along the way, we find a Burling-Lax-Halmos type of result for a triple of multiplication operators acting on vector-valued Hardy spaces. In both the model theory and unitary invariance, fundamental operators play a fundamental role. This thesis answers the question when two operators F and G with w(F ) and w(G) no greater than one, are admissible as fundamental operators, in other words, when there exists a -contraction (S; P ) such that F is the fundamental operator of (S; P ) and G is the fundamental operator of (S ; P ). This thesis also answers a similar question in the tetra block setting.
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Chen, Chun Ming, and 陳駿銘. "The Graphics of Symmetrized Bidiscs and Spectral Interpolating Functions." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/85112132699826651919.

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碩士
東海大學
數學系
98
The symmetrrized bidisc is defined as the set of two coefficients of a quadratic equation with its roots located inside the unit disc. In this thesis, a matlab-based GUI is developed to the graphs of the symmetrized bidisc and associated spectral interpolating functions. Since the symmetrized bidisc belongs to C^2, its 3D projection is plotted as the real or imaginary part of one variable is fixed. By the way, the graph of the symmetrized bidisc is also shown when the radius of the root's location changes. Furthermorre, two kinds of approaches are used to construct the spectral interoplating function defined on the symmetrized bidisc are introduced and their graphs are depicted as well. Once the interpolating function is computed, we demo how to construct the interpolation function to solve the two-by-two spectral Nevanlinna-Pick problem. Keywords: unit disc, symmetrized bidisc, quadratic equation, matlab, GUI, spectral Nevanlinna- Pick interpolation problemn
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Books on the topic "Symmetrized bidisk"

1

Young, Nicholas, Jim Agler, and Zinaida Lykova. Geodesics, Retracts, and the Norm-Preserving Extension Property in the Symmetrized Bidisc. American Mathematical Society, 2019.

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Book chapters on the topic "Symmetrized bidisk"

1

Agler, Jim, Zinaida A. Lykova, and N. J. Young. "Carathéodory extremal functions on the symmetrized bidisc." In Operator Theory, Analysis and the State Space Approach, 1–21. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-04269-1_1.

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Agler, J., F. B. Yeh, and N. J. Young. "Realization of Functions into the Symmetrised Bidisc." In Reproducing Kernel Spaces and Applications, 1–37. Basel: Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-8077-0_1.

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3

"Model Theory on the Symmetrized Bidisc." In Operator Analysis, 169–88. Cambridge University Press, 2020. http://dx.doi.org/10.1017/9781108751292.008.

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Journal articles
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