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Relevant bibliographies by topics / Multivariate Operator Theory

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Journal articles

Academic literature on the topic 'Multivariate Operator Theory'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Multivariate Operator Theory"

1

Xu, Yuan. "Multivariate orthogonal polynomials and operator theory." Transactions of the American Mathematical Society 343, no. 1 (1994): 193–202. http://dx.doi.org/10.1090/s0002-9947-1994-1169912-x.

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2

Anastassiou, George A. "Multivariate and abstract approximation theory for Banach space valued functions." Demonstratio Mathematica 50, no. 1 (2017): 208–22. http://dx.doi.org/10.1515/dema-2017-0020.

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Abstract Here we study quantitatively the high degree of approximation of sequences of linear operators acting on Banach space valued Fréchet differentiable functions to the unit operator, as well as other basic approximations including those under convexity. These operators are bounded by real positive linear companion operators. The Banach spaces considered here are general and no positivity assumption is made on the initial linear operators for which we study their approximation properties. We derive pointwise and uniform estimates, which imply the approximation of these operators to the unit assuming Fréchet differentiability of functions, and then we continue with basic approximations. At the end we study the special case where the approximated function fulfills a convexity condition resulting into sharp estimates. We give applications to Bernstein operators.

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3

Filipiak, Katarzyna, Daniel Klein, and Erika Vojtková. "The properties of partial trace and block trace operators of partitioned matrices." Electronic Journal of Linear Algebra 33 (May 16, 2018): 3–15. http://dx.doi.org/10.13001/1081-3810.3688.

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The aim of this paper is to give the properties of two linear operators defined on non-square partitioned matrix: the partial trace operator and the block trace operator. The conditions for symmetry, nonnegativity, and positive-definiteness are given, as well as the relations between partial trace and block trace operators with standard trace, vectorizing and the Kronecker product operators. Both partial trace as well as block trace operators can be widely used in statistics, for example in the estimation of unknown parameters under the multi-level multivariate models or in the theory of experiments for the determination of an optimal designs under the linear models.

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4

Fuchs, David, Steven Sherwood, and Daniel Hernandez. "An Exploration of Multivariate Fluctuation Dissipation Operators and Their Response to Sea Surface Temperature Perturbations." Journal of the Atmospheric Sciences 72, no. 1 (2015): 472–86. http://dx.doi.org/10.1175/jas-d-14-0077.1.

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Abstract The fluctuation–dissipation theorem (FDT) has been proposed as a method of calculating the mean response of the atmosphere to small external perturbations. This paper explores the application of the theory under time and space constraints that approximate realistic conditions. To date, most applications of the theory in the climate context used univariate, low-dimensional-state representations of the climate system and an arbitrarily long sample size. The authors explore high-dimensional multivariate FDT operators and the lower bounds of sample size needed to construct skillful operators. It is shown that the skill of the operator depends on the selection of variables and features representing the climate system and that these features change once memory (slab ocean) is added to the system. In addition, it is found that the FDT operator has skill in estimating the response to realistic sea surface temperature (SST) patterns, such as El Niño–Southern Oscillation (ENSO), despite the fact that these patterns were not part of the data used to produce the operator. The response of clouds is also studied; for variables that represent cloud properties, the decrease in skill in relation to decrease in sample size still maintains the key features of the response.

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5

Hiai, Fumio, Yuki Seo, and Shuhei Wada. "Ando–Hiai type inequalities for multivariate operator means." Linear and Multilinear Algebra 67, no. 11 (2018): 2253–81. http://dx.doi.org/10.1080/03081087.2018.1488938.

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6

Neretin, Yury A. "Multi-operator colligations and multivariate characteristic functions." Analysis and Mathematical Physics 1, no. 2-3 (2011): 121–38. http://dx.doi.org/10.1007/s13324-011-0009-y.

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7

Reich, Nils. "Anisotropic Operator Symbols Arising From Multivariate Jump Processes." Integral Equations and Operator Theory 63, no. 1 (2008): 127–50. http://dx.doi.org/10.1007/s00020-008-1645-y.

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8

Zizler, Peter. "The spectral radius of a multivariate sampling operator." Linear Algebra and its Applications 385 (July 2004): 463–74. http://dx.doi.org/10.1016/j.laa.2003.12.042.

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9

Chen, Zhong Yin. "The Traits of Two-Directional Orthogonal Multivariate Small-Wave Packages with Finite Support." Advanced Materials Research 430-432 (January 2012): 543–46. http://dx.doi.org/10.4028/www.scientific.net/amr.430-432.543.

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In this paper, we introduce the notion of vector-valued multiresolution analysis and two-directional vector-valued multivariate wavelet packages associated with an integer-valued dilation matrix. A novel method for constructing multi-dimensional vector-valued wavelet packet is presented. Their characteristics are researched by means of operator theory, time-frequency analysis method and matrix theory. Three orthogonality formulas concerning the wavelet packets are establ- lished. Orthogonality decomposition relation formulas of the space are derived by constru- cting a series of subspaces of wavelet packets.

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10

Xia, Yin Hong, and Hua Li. "The Characterization of a Kind of Vector-Valued Multivariate Wavelet Packets with Composite Dilation Matrix." Key Engineering Materials 439-440 (June 2010): 932–37. http://dx.doi.org/10.4028/www.scientific.net/kem.439-440.932.

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In this article, the notion of a kind of multivariate vector-valued wavelet packets with composite dilation matrix is introduced. A new method for designing a kind of biorthogonal vector- valued wavelet packets in higher dimensions is developed and their biorthogonality property is inv- -estigated by virtue of matrix theory, time-frequency analysis method, and operator theory. Two biorthogonality formulas concerning these wavelet packets are presented. Moreover, it is shown how to gain new Riesz bases of space by constructing a series of subspace of wavelet packets.

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