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A review on spectral data preprocessing techniques for machine learning and quantitative analysis. [PDF]

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Yan C.
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Dual truncated Toeplitz operators

Journal of Mathematical Analysis and Applications, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xuanhao Ding
exaly   +2 more sources

Invertibility and spectral properties of dual Toeplitz operators

Journal of Mathematical Analysis and Applications, 2020
Consider \(L_2(\mathbb{D})\), where \(\mathbb{D}\) is the unit disk on the complex plane, and its Bergman subspace \(L^2_a\) consisting of analytic functions. Let \(P\) be the orthogonal projection of \(L_2(\mathbb{D})\) onto \(L^2_a\). Given \(\varphi \in L^{\infty}(\mathbb{D})\), the dual Toeplitz operator \(S_{\varphi}\) with symbol \(\varphi\) is ...
Xuanhao Ding
exaly   +3 more sources

Dual Toeplitz operators on the sphere

Acta Mathematica Sinica, English Series, 2013
The paper is devoted to the systematic study of dual Toeplitz operators on the orthogonal complement of the Hardy space of the unit sphere in \(\mathbb{C}^n\). A criterion of commutativity of two dual Toeplitz operators is obtained. A criterion guaranteeing that the product of two dual Toeplitz operators is again a dual Toeplitz operator is also ...
Hocine Guediri
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Dual Toeplitz Operators on the Orthogonal Complement of the Harmonic Bergman Space

Acta Mathematica Sinica, English Series, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Peng, Yang, Zhao, Xian Feng
exaly   +3 more sources

The commutant and invariant subspaces for dual truncated Toeplitz operators

Banach Journal of Mathematical Analysis, 2020
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Xuanhao Ding
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Commuting dual Toeplitz operators on the orthogonal complement of the Dirichlet space

Acta Mathematica Sinica, English Series, 2009
Let \(D\) be the open unit disk in the complex plane and let \(dA\) denote the normalized Lebesgue measure. The Sobolev space \(W^{1,2}\) consists of functions \(u:D\to\mathbb{C}\) with the weak partial derivatives of order 1 and the norm \[ \|u\|_{\frac{1}{2}}=\left(\left|\int_D u dA\right|^2+\int_D\left(\left|\frac{\partial u}{\partial z}\right|^2 ...
Tao Yu
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Algebraic properties of dual Toeplitz operators on the orthogonal complement of the Dirichlet space

Acta Mathematica Sinica, English Series, 2008
The Dirichlet space \({\mathcal D}\) is the space of all analytic functions in the unit disk that belong to the Sobolev space \(W^{1,2}\). Let \(Q\) denote the projection of \(W^{1,2}\) onto \({\mathcal D}^\perp\). For a function \(\varphi\) in the Sobolev space \(W^{1,\infty}\), let \(S_\varphi\) denote the dual Toeplitz operator defined by \(S_ ...
Tao Yu
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Commuting dual Toeplitz operators on weighted Bergman spaces of the unit ball

Acta Mathematica Sinica, English Series, 2011
Let \(A^2_{\alpha}(B_n)\) be the standard weighted Bergman space over the unit ball \(B_n\) in \(\mathbb{C}^n\), and let \(P_{\alpha}\) be the corresponding Bergman projection. For a function \(f \in L^{\infty}(B_n)\), the dual Toeplitz operator is defined by \(S_fu = (I-P_{\alpha})(fu)\), for \(u \in (A^2_{\alpha}(B_n))^{\perp}\).
Yu Feng Lu, Lu Yu Feng
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