Relevant bibliographies by topics / Local Riesz transforms

Academic literature on the topic 'Local Riesz transforms'

Author: Grafiati
Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Local Riesz transforms"

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Peloso, Marco M., and Silvia Secco. "Local Riesz transforms characterization of local Hardy spaces." Collectanea mathematica 59, no. 3 (October 2008): 299–320. http://dx.doi.org/10.1007/bf03191189.

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Zhu, Hua. "Riesz Transform Characterization of Weighted Hardy Spaces Associated with Schrödinger Operators." Journal of Function Spaces 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/2856103.

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We characterize the weighted local Hardy spaceshρ1(ω)related to the critical radius functionρand weightsω∈A1ρ,∞(Rn)by localized Riesz transformsR^j; in addition, we give a characterization of weighted Hardy spacesHL1(ω)via Riesz transforms associated with Schrödinger operatorL, whereL=-Δ+Vis a Schrödinger operator onRn(n≥3) andVis a nonnegative function satisfying the reverse Hölder inequality.
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Zhu, Hua. "Weighted Weak Local Hardy Spaces Associated with Schrödinger Operators." Journal of Function Spaces 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/490259.

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We characterize the weighted weak local Hardy spacesWhρp(ω)related to the critical radius functionρand weightsω∈A∞ρ,∞(Rn)which locally behave as Muckenhoupt’s weights and actually include them, by the atomic decomposition. As an application, we show that localized Riesz transforms are bounded on the weighted weak local Hardy spaces.
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Dai, Feng, and Wenrui Ye. "Local restriction theorem and maximal Bochner-Riesz operators for the Dunkl transforms." Transactions of the American Mathematical Society 371, no. 1 (June 26, 2018): 641–79. http://dx.doi.org/10.1090/tran/7285.

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Zhang, Lin, and Hongyu Li. "Encoding local image patterns using Riesz transforms: With applications to palmprint and finger-knuckle-print recognition." Image and Vision Computing 30, no. 12 (December 2012): 1043–51. http://dx.doi.org/10.1016/j.imavis.2012.09.003.

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Cao, Jun, Svitlana Mayboroda, and Dachun Yang. "Local Hardy spaces associated with inhomogeneous higher order elliptic operators." Analysis and Applications 15, no. 02 (January 25, 2017): 137–224. http://dx.doi.org/10.1142/s0219530515500189.

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Let [Formula: see text] be a divergence form inhomogeneous higher order elliptic operator with complex bounded measurable coefficients. In this paper, for all [Formula: see text] and [Formula: see text] satisfying a weak ellipticity condition, the authors introduce the local Hardy spaces [Formula: see text] associated with [Formula: see text], which coincide with Goldberg’s local Hardy spaces [Formula: see text] for all [Formula: see text] when [Formula: see text] (the Laplace operator). The authors also establish a real-variable theory of [Formula: see text], which includes their characterizations in terms of the local molecules, the square functions or the maximal functions, the complex interpolation and dual spaces. These real-variable characterizations on the local Hardy spaces are new even when [Formula: see text] (the divergence form homogeneous second-order elliptic operator). Moreover, the authors show that [Formula: see text] coincides with the Hardy space [Formula: see text] associated with the operator [Formula: see text] for all [Formula: see text], where [Formula: see text] is some positive constant depending on the ellipticity and the off-diagonal estimates of [Formula: see text]. As an application, the authors establish some mapping properties for the local Riesz transforms [Formula: see text] on [Formula: see text], where [Formula: see text] and [Formula: see text].
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Huang, Jizheng, and Yu Liu. "Molecular Characterization of Hardy Spaces Associated with Twisted Convolution." Journal of Function Spaces 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/326940.

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Seelamantula, Chandra Sekhar, Nicolas Pavillon, Christian Depeursinge, and Michael Unser. "Local demodulation of holograms using the Riesz transform with application to microscopy." Journal of the Optical Society of America A 29, no. 10 (September 17, 2012): 2118. http://dx.doi.org/10.1364/josaa.29.002118.

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Yazdi, Mehran, and Hamed Erfankhah. "Multiclass histology image retrieval, classification using Riesz transform and local binary pattern features." Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization 8, no. 6 (May 13, 2020): 595–607. http://dx.doi.org/10.1080/21681163.2020.1761885.

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Hai, Dinh Nguyen Duy. "Filter regularization method for a nonlinear Riesz-Feller space-fractional backward diffusion problem with temporally dependent thermal conductivity." Fractional Calculus and Applied Analysis 24, no. 4 (August 1, 2021): 1112–29. http://dx.doi.org/10.1515/fca-2021-0048.

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Abstract This paper concerns a backward problem for a nonlinear space-fractional diffusion equation with temporally dependent thermal conductivity. Such a problem is obtained from the classical diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order α ∈ (0, 2), which is usually used to model the anomalous diffusion. We show that the problem is severely ill-posed. Using the Fourier transform and a filter function, we construct a regularized solution from the data given inexactly and explicitly derive the convergence estimate in the case of the local Lipschitz reaction term. Special cases of the regularized solution are also presented. These results extend some earlier works on the space-fractional backward diffusion problem.
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Dissertations / Theses on the topic "Local Riesz transforms"

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Marchant, Ross Glenn Raymond. "Local feature analysis using higher-order Riesz transforms." Thesis, 2016. https://researchonline.jcu.edu.au/46047/1/46047-marchant-2016-thesis.pdf.

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Rich descriptions of local image structures are important for higher-level understanding of images in computer vision. Phase-based representations allow the discrimination of symmetric features, such as lines, and anti-symmetric features, such as edges, independent of their strength. Methods to obtain phase information include quadrature filters using the Hilbert transform, spherical quadrature filters using the Riesz transform, and 2D analytic signals such as the monogenic signal and signal multi-vector. This thesis develops a new local image descriptor, called the circular harmonic vector, consisting of the higher-order Riesz transforms of an image. The circular harmonic vector describes the symmetries of the local image structure. It extends previous analytic signals, and is formulated in the context of 2D steerable wavelet frames. Methods are introduced to solve for the parameters of a general signal model by splitting the circular harmonic vector into model and residual components. In particular, the super-resolution method, normally used for the resolving of spike trains, can be applied. The methods are applied to estimating the parameters of sinusoidal, multi-sinusoidal and half-sinusoidal phase-based image models. The sinusoidal model describes lines and edges in terms of amplitude, phase and orientation. Using higher-order Riesz transforms in the circular harmonic vector gives better parameter estimates, and the residual component is used to develop a new detection measure for junctions and corners. The multi-sinusoidal model is applied to coral core x-ray analysis, from which separate reconstruction of features is possible as a result of the wavelet basis. The half-sinusoidal model is used to obtain the amplitudes and orientations of the line and edge segments in junctions and corners, with phase discriminating their type. Finally, a new representation of local image structure through scale is introduced. It describes the continuous response of the circular harmonic vector response shifted though scale in the form of a quaternion-valued matrix. The matrix is derived from the higher-order Riesz transforms of an isotropic wavelet frame given by Fourier series basis functions in the logarithmic frequency domain. New measures for scale selection are developed, along with a continuous version of phase congruency that is combined with previous image models to detect and discriminate image features in an illumination invariant way.
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Morris, Andrew Jordan. "Local Hardy spaces and quadratic estimates for Dirac type operators on Riemannian manifolds." Phd thesis, 2010. http://hdl.handle.net/1885/8864.

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The connection between quadratic estimates and the existence of a bounded holomorphic functional calculus of an operator provides a framework for applying harmonic analysis to the theory of differential operators. This is a generalization of the connection between Littlewood--Paley--Stein estimates and the functional calculus provided by the Fourier transform. We use the former approach in this thesis to study first-order differential operators on Riemannian manifolds. The theory developed is local in the sense that it does not depend on the spectrum of the operator in a neighbourhood of the origin. When we apply harmonic analysis to obtain estimates, the local theory only requires that we do so up to a finite scale. This allows us to consider manifolds with exponential volume growth in situations where the global theory requires polynomial volume growth. A holomorphic functional calculus is constructed for operators on a reflexive Banach space that are bisectorial except possibly in a neighbourhood of the origin. We prove that this functional calculus is bounded if and only if certain local quadratic estimates hold. For operators with spectrum in a neighbourhood of the origin, the results are weaker than those for bisectorial operators. For operators with a spectral gap in a neighbourhood of the origin, the results are stronger. In each case, however, local quadratic estimates are a more appropriate tool than standard quadratic estimates for establishing that the functional calculus is bounded. This theory allows us to define local Hardy spaces of differential forms that are adapted to a class of first-order differential operators on a complete Riemannian manifold with at most exponential volume growth. The local geometric Riesz transform associated with the Hodge--Dirac operator is bounded on these spaces provided that a certain condition on the exponential growth of the manifold is satisfied. A characterisation of these spaces in terms of local molecules is also obtained. These results can be viewed as the localisation of those for the Hardy spaces of differential forms introduced by Auscher, McIntosh and Russ. Finally, we introduce a class of first-order differential operators that act on the trivial bundle over a complete Riemannian manifold with at most exponential volume growth and on which a local Poincar\'{e} inequality holds. A local quadratic estimate is established for certain perturbations of these operators. As an application, we solve the Kato square root problem for divergence form operators on complete Riemannian manifolds with Ricci curvature bounded below that are embedded in Euclidean space with a uniformly bounded second fundamental form. This is based on the framework for Dirac type operators that was introduced by Axelsson, Keith and McIntosh.
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Book chapters on the topic "Local Riesz transforms"

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Bülow, Thomas, Dieter Pallek, and Gerald Sommer. "Riesz Transforms for the Isotropic Estimation of the Local Phase of Moire Interferograms." In Informatik aktuell, 333–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-59802-9_42.

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Conference papers on the topic "Local Riesz transforms"

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Marchant, Ross, and Paul Jackway. "Local feature analysis using a sinusoidal signal model derived from higher-order Riesz transforms." In 2013 20th IEEE International Conference on Image Processing (ICIP). IEEE, 2013. http://dx.doi.org/10.1109/icip.2013.6738720.

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Malutan, Raul, Simina Emerich, Septimiu Crisan, Olimpiu Pop, and Laszlo Lefkovits. "Dorsal hand vein recognition based on Riesz Wavelet Transform and Local Line Binary Pattern." In 2017 3rd International Conference on Frontiers of Signal Processing (ICFSP). IEEE, 2017. http://dx.doi.org/10.1109/icfsp.2017.8097159.

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