Academic literature on the topic 'Toeplitz operators'

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Journal articles on the topic "Toeplitz operators"

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Jurasik, Joanna, and Bartosz Łanucha. "Asymmetric truncated Toeplitz operators equal to the zero operator." Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica 70, no. 2 (December 24, 2016): 51. http://dx.doi.org/10.17951/a.2016.70.2.51.

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Asymmetric truncated Toeplitz operators are compressions of multiplication operators acting between two model spaces. These operators are natural generalizations of truncated Toeplitz operators. In this paper we describe symbols of asymmetric truncated Toeplitz operators equal to the zero operator.
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Murphy, G. J. "Toeplitz Operators." Irish Mathematical Society Bulletin 0022 (1989): 42–49. http://dx.doi.org/10.33232/bims.0022.42.49.

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Zhang, Bo, Yanyue Shi, and Yufeng Lu. "Algebraic Properties of Toeplitz Operators on the Polydisk." Abstract and Applied Analysis 2011 (2011): 1–18. http://dx.doi.org/10.1155/2011/962313.

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We discuss some algebraic properties of Toeplitz operators on the Bergman space of the polydiskDn. Firstly, we introduce Toeplitz operators with quasihomogeneous symbols and property (P). Secondly, we study commutativity of certain quasihomogeneous Toeplitz operators and commutators of diagonal Toeplitz operators. Thirdly, we discuss finite rank semicommutators and commutators of Toeplitz operators with quasihomogeneous symbols. Finally, we solve the finite rank product problem for Toeplitz operators on the polydisk.
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Agbor, Dieudonne. "Algebraic Properties of Toeplitz Operators on the Pluri-harmonic Fock Space." Journal of Mathematics Research 9, no. 6 (October 26, 2017): 67. http://dx.doi.org/10.5539/jmr.v9n6p67.

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We study some algebraic properties of Toeplitz operators with radial and quasi homogeneous symbols on the pluriharmonic Fock space over $\mathbb{C}^{n}$. We determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator, the zero-product problem for the product of two Toeplitz operators. Next we characterize the commutativity of Toeplitz operators with quasi homogeneous symbols and finally we study finite rank of the product of Toeplitz operators with quasi homogeneous symbols.
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Gu, Caixing, Dong-O. Kang, Eungil Ko, and Ji Eun Lee. "Binormal Toeplitz operators on the Hardy space." International Journal of Mathematics 30, no. 01 (January 2019): 1950001. http://dx.doi.org/10.1142/s0129167x19500010.

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We characterize binormal Toeplitz operators with analytic, or, coanalytic symbol functions. Furthermore, for a large class of nonanalytic, noncoanalytic Toeplitz operators which include Toeplitz operators with trigonometric or rational symbols, we prove that those Toeplitz operators are binormal if and only if they are normal. Some of the historically important examples of Toeplitz operators in the paper show that our problem is subtle and the above result is sharp.
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Yang, Jingyu, Liu Liu, and Yufeng Lu. "Algebraic Properties of Toeplitz Operators on the Pluriharmonic Bergman Space." Journal of Function Spaces and Applications 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/578436.

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We study some algebraic properties of Toeplitz operators with radial or quasihomogeneous symbols on the pluriharmonic Bergman space. We first give the necessary and sufficient conditions for the product of two Toeplitz operators with radial symbols to be a Toeplitz operator and discuss the zero-product problem for several Toeplitz operators with radial symbols. Next, we study the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols. Finally, we also investigate finite rank commutators and semicommutators of two Toeplitz operators with quasihomogeneous symbols.
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Nikpour, Mehdi. "On Some Algebraic and Operator-Theoretic Properties of λ-Toeplitz Operators." Journal of Operators 2015 (January 6, 2015): 1–8. http://dx.doi.org/10.1155/2015/172754.

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Based on a spectral problem raised by Barría and Halmos, a new class of Hardy-Hilbert space operators, containing the classical Toeplitz operators, is introduced, and some of their Toeplitz-like algebraic and operator-theoretic properties are studied and explored.
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Nakazi, Takahiko. "Absolute Values of Toeplitz Operators and Hankel Operators." Canadian Mathematical Bulletin 34, no. 2 (June 1, 1991): 249–53. http://dx.doi.org/10.4153/cmb-1991-040-1.

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AbstractNehari's theorem for norms of bounded Hankel operators is revisited. Using it, the absolute values of Toeplitz operators are studied. This gives a theorem of Widom and Devinatz for invertible Toeplitz operators.
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Liu, Lanzhe. "Weighted boundedness for Toeplitz type operator associated to general integral operators." Asian-European Journal of Mathematics 07, no. 02 (June 2014): 1450026. http://dx.doi.org/10.1142/s1793557114500260.

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In this paper, we establish the weighted sharp maximal function estimates for the Toeplitz type operators associated to some integral operators and the weighted Lipschitz and BMO functions. As an application, we obtain the boundedness of the Toeplitz type operators on weighted Lebesgue and Morrey spaces. The operator includes Littlewood–Paley operator, Marcinkiewicz operator and Bochner–Riesz operator.
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Engliš, Miroslav. "Toeplitz operators and localization operators." Transactions of the American Mathematical Society 361, no. 02 (August 18, 2008): 1039–52. http://dx.doi.org/10.1090/s0002-9947-08-04547-9.

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Dissertations / Theses on the topic "Toeplitz operators"

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Ordonez-Delgado, Bartleby. "Algebras of Toeplitz Operators." Thesis, Virginia Tech, 2006. http://hdl.handle.net/10919/32378.

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In this work we examine C*-algebras of Toeplitz operators over the unit ball in C^n and the unit polydisc in C^2. Toeplitz operators are interesting examples of non-normal operators that generate non-commutative C*-algebras. Moreover, in the nice cases (depending on the geometry of the domain) of algebras of Toeplitz operators we can recover some analogues of the spectral theorem up to compact operators. In this setting, we can capture the index of a Fredholm operator which is a fundamental numerical invariant in Operator Theory.
Master of Science
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Fedchenko, Dmitry, and Nikolai Tarkhanov. "An index formula for Toeplitz operators." Universität Potsdam, 2014. http://opus.kobv.de/ubp/volltexte/2014/7249/.

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We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first order partial differential equations in a bounded domain of Euclidean space with infinitely differentiable boundary.
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Deleporte-Dumont, Alix. "Low-energy spectrum of Toeplitz operators." Thesis, Strasbourg, 2019. http://www.theses.fr/2019STRAD004/document.

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Les opérateurs de Berezin--Toeplitz permettent de quantifier des fonctions, ou des symboles, sur des variétés kähleriennes compactes, et sont définies à partir du noyau de Bergman (ou de Szeg\H{o}). Nous étudions le spectre des opérateurs de Toeplitz dans un régime asymptotique qui correspond à une limite semiclassique. Cette étude est motivée par le comportement magnétique atypique observé dans certains cristaux à basse température. Nous étudions la concentration des fonctions propres des opérateurs de Toeplitz, dans des cas où les effets sous-principaux (du même ordre que le paramètre semiclassique) permet de différencier entre plusieurs configurations classiques, un effet connu en physique sous le nom de sélection quantique Nous exhibons un critère général pour la sélection quantique et nous donnons des développements asymptotiques précis de fonctions propres dans le cas Morse et Morse--Bott, ainsi que dans un cas dégénéré. Nous développons également un nouveau cadre pour le traitement du noyau de Bergman et des opérateurs de Toeplitz en régularité analytique. Nous démontrons que le noyau de Bergman admet un développement asymptotique, avec erreur exponentiellement petite, sur des variétés analytiques réelles. Nous obtenons aussi une précision exponentiellement fine dans les compositions et le spectre d'opérateurs à symbole analytique, et la décroissance exponentielle des fonctions propres
Berezin-Toeplitz operators allow to quantize functions, or symbols, on compact Kähler manifolds, and are defined using the Bergman (or Szeg\H{o}) kernel. We study the spectrum of Toeplitz operators in an asymptotic regime which corresponds to a semiclassical limit. This study is motivated by the atypic magnetic behaviour observed in certain crystals at low temperature. We study the concentration of eigenfunctions of Toeplitz operators in cases where subprincipal effects (of same order as the semiclassical parameter) discriminate between different classical configurations, an effect known in physics as quantum selection . We show a general criterion for quantum selection and we give detailed eigenfunction expansions in the Morse and Morse-Bott case, as well as in a degenerate case. We also develop a new framework in order to treat Bergman kernels and Toeplitz operators with real-analytic regularity. We prove that the Bergman kernel admits an expansion with exponentially small error on real-analytic manifolds. We also obtain exponential accuracy in compositions and spectra of operators with analytic symbols, as well as exponential decay of eigenfunctions
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Fedchenko, Dmitry, and Nikolai Tarkhanov. "A Class of Toeplitz Operators in Several Variables." Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2013/6893/.

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We introduce the concept of Toeplitz operator associated with the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We characterise those Toeplitz operators which are Fredholm, thus initiating the index theory.
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Vasaturo, Anthony P. Vasaturo. "Invertibility of Toeplitz Operators via Berezin Transforms." University of Toledo / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1529951538729292.

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Gaebler, David. "Toeplitz Operators on Locally Compact Abelian Groups." Scholarship @ Claremont, 2004. https://scholarship.claremont.edu/hmc_theses/163.

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Given a function (more generally, a measure) on a locally compact Abelian group, one can define the Toeplitz operators as certain integral transforms of functions on the dual group, where the kernel is the Fourier transform of the original function or measure. In the case of the unit circle, this corresponds to forming a matrix out of the Fourier coefficients in a particular way. We will study the asymptotic eigenvalue distributions of these Toeplitz operators.
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Schulze, Bert-Wolfgang, and Nikolai Tarkhanov. "Boundary value problems with Toeplitz conditions." Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2009/2983/.

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We describe a new algebra of boundary value problems which contains Lopatinskii elliptic as well as Toeplitz type conditions. These latter are necessary, if an analogue of the Atiyah-Bott obstruction does not vanish. Every elliptic operator is proved to admit up to a stabilisation elliptic conditions of such a kind. Corresponding boundary value problems are then Fredholm in adequate scales of spaces. The crucial novelty consists of the new type of weighted Sobolev spaces which serve as domains of pseudodifferential operators and which fit well to the nature of operators.
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Ordonez-Delgado, Bartleby. "An Embedded Toeplitz Problem." Diss., Virginia Tech, 2010. http://hdl.handle.net/10919/29007.

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In this work we investigate multi-variable Toeplitz operators and their relationship with KK-theory in order to apply this relationship to define and analyze embedded Toeplitz problems. In particular, we study the embedded Toeplitz problem of the unit disk into the unit ball in C^2. The embedding of Toeplitz problems suggests a way to define Toeplitz operators over singular spaces.
Ph. D.
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Nikpour, Mehdi. "Toeplitzness of Composition Operators and Parametric Toeplitzness." University of Toledo / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1346951238.

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Ehrhardt, Torsten. "Factorization theory for Toeplitz plus Hankel operators and singular integral operators with flip." Doctoral thesis, [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=972573305.

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Books on the topic "Toeplitz operators"

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1941-, Silbermann Bernd, ed. Analysis of Toeplitz operators. Berlin: Akademie-Verlag Berlin, 1989.

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Böttcher, Albrecht. Analysis of Toeplitz operators. Berlin: Springer-Verlag, 1990.

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Böttcher, Albrecht, and Bernd Silbermann. Analysis of Toeplitz Operators. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-662-02652-6.

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Bauer, Wolfram, Roland Duduchava, Sergei Grudsky, and Marinus A. Kaashoek, eds. Operator Algebras, Toeplitz Operators and Related Topics. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44651-2.

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Bini, Dario A., Torsten Ehrhardt, Alexei Yu Karlovich, and Ilya Spitkovsky, eds. Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49182-0.

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Barron, Tatyana. Toeplitz Operators on Kähler Manifolds. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94292-6.

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Basor, E. L., and I. Gohberg, eds. Toeplitz Operators and Related Topics. Basel: Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-8543-0.

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Basor, Estelle, Albrecht Böttcher, Torsten Ehrhardt, and Craig A. Tracy, eds. Toeplitz Operators and Random Matrices. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-13851-5.

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1949-, Karlovich Yuri I., ed. Carleson curves, Muckenhoupt weights, and Toeplitz operators. Basel: Birkhäuser Verlag, 1997.

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Nikolskii, N. K., ed. Toeplitz Operators and Spectral Function Theory. Basel: Birkhäuser Basel, 1989. http://dx.doi.org/10.1007/978-3-0348-5587-7.

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Book chapters on the topic "Toeplitz operators"

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Douglas, Ronald G. "Toeplitz Operators." In Graduate Texts in Mathematics, 158–84. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1656-8_7.

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Peller, Vladimir. "Toeplitz Operators." In Springer Monographs in Mathematics, 87–123. New York, NY: Springer New York, 2003. http://dx.doi.org/10.1007/978-0-387-21681-2_3.

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Zhu, Kehe. "Toeplitz Operators." In Analysis on Fock Spaces, 213–66. Boston, MA: Springer US, 2012. http://dx.doi.org/10.1007/978-1-4419-8801-0_6.

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Böttcher, Albrecht, Yuri I. Karlovich, and Ilya M. Spitkovsky. "Toeplitz Operators." In Convolution Operators and Factorization of Almost Periodic Matrix Functions, 301–21. Basel: Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8152-4_16.

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Axler, Sheldon. "Toeplitz Operators." In A Glimpse at Hilbert Space Operators, 125–33. Basel: Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0346-0347-8_9.

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Guillemin, V. W. "Toeplitz Operators." In Louis Boutet de Monvel, Selected Works, 585–713. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-27909-1_8.

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Gohberg, I., M. A. Kaashoek, and S. Goldberg. "Block Toeplitz Operators." In Classes of Linear Operators Vol. II, 562–82. Basel: Birkhäuser Basel, 1993. http://dx.doi.org/10.1007/978-3-0348-8558-4_5.

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Le Floch, Yohann. "Berezin–Toeplitz Operators." In CRM Short Courses, 55–62. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94682-5_5.

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Upmeier, Harald. "Toeplitz Operators and Toeplitz C*-Algebras." In Toeplitz Operators and Index Theory in Several Complex Variables, 241–370. Basel: Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-9246-9_4.

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Sarason, Donald. "Kernels of Toeplitz Operators." In Toeplitz Operators and Related Topics, 153–64. Basel: Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-8543-0_10.

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Conference papers on the topic "Toeplitz operators"

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"I.5 Toeplitz and Toeplitz-like Operators." In Proceedings of the 5th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812835635_others02.

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Falk, Kevin. "Spectral triples and Toeplitz operators." In Frontiers of Fundamental Physics 14. Trieste, Italy: Sissa Medialab, 2016. http://dx.doi.org/10.22323/1.224.0140.

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Turcajova, Radka, and Jaroslav Kautsky. "Block Toeplitz-like operators and multiwavelets." In SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use Photonics, edited by Harold H. Szu. SPIE, 1995. http://dx.doi.org/10.1117/12.205454.

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Grudsky, S., and N. Vasilevski. "Dynamics of Spectra of Toeplitz Operators." In Proceedings of the 4th International ISAAC Congress. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701732_0045.

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Vasilevski, Nikolai, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Commutative Algebras of Toeplitz Operators in Action." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3637748.

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ZORBOSKA, N. "MULTIPLICATION AND TOEPLITZ OPERATORS ON THE ANALYTIC BESOV SPACES." In Proceedings of the 5th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812835635_0036.

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Shatarah, Amani. "Slant Toeplitz like Operators on The Lebesgue Space of The Torus." In 2021 International Conference on Information Technology (ICIT). IEEE, 2021. http://dx.doi.org/10.1109/icit52682.2021.9491674.

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Tu, Stephen, Ross Boczar, and Benjamin Recht. "On the Approximation of Toeplitz Operators for Nonparametric $\mathcal{H}_{\infty}$-norm Estimation." In 2018 Annual American Control Conference (ACC). IEEE, 2018. http://dx.doi.org/10.23919/acc.2018.8431846.

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Bercovici, Hari, Ciprion Foias, and Allen Tannenbaum. "On skew Toeplitz operations, I." In 26th IEEE Conference on Decision and Control. IEEE, 1987. http://dx.doi.org/10.1109/cdc.1987.272697.

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Galatsanos, Nikolas P., and Aggelos K. Katsaggelos. "An Analysis of Regularized Linear Image Recovery." In Signal Recovery and Synthesis. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/srs.1992.wc2.

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In many applications that necessitate image recovery the imaging system can be modeled as a convolution of the original image with an ill-posed operator and then adding noise. We assume that the M×M original image is blurred by a space-invariant convolution operator and independent identically distributed (i.i.d.) zero mean additive noise described by the model where H is a M2×M2 Toeplitz matrix modeling the space-invariant blur, the vectors g, f, and n are M2×1 lexicographic orders of the degraded observed image, the original image and the noise, respectively.
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