Relevant bibliographies by topics / Bilinear Hilbert transform

Academic literature on the topic 'Bilinear Hilbert transform'

Author: Grafiati
Published: 10 December 2022
Last updated: 29 January 2023

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Journal articles on the topic "Bilinear Hilbert transform"

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Buchkovska, Aneta L., and Stevan PilipoviĆ. "Bilinear Hilbert Transform of Ultradistributions." Integral Transforms and Special Functions 13, no. 3 (January 2002): 211–21. http://dx.doi.org/10.1080/10652460213520.

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Shi, Zuoshunhua, and Dunyan Yan. "Criterion onLp1×Lp2→Lq-Boundedness for Oscillatory Bilinear Hilbert Transform." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/712051.

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We investigate the bilinear Hilbert transform with oscillatory factors and the truncated bilinear Hilbert transform. The main result is that theLp1×Lp2→Lq-boundedness of the two operators is equivalent with1≤p1,p2<∞, and1/q=1/p1+1/p2. In addition, we also discuss the boundedness of a variant operator of bilinear Hilbert transform with a nontrivial polynomial phase.
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Bučkovska, Aneta, Stevan Pilipović, and Mirjana Vuković. "Inversion theorem for bilinear Hilbert transform." Integral Transforms and Special Functions 19, no. 5 (May 2008): 317–25. http://dx.doi.org/10.1080/10652460701855948.

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Blasco, O., M. Carro, and T. A. Gillespie. "Bilinear Hilbert Transform on Measure Spaces." Journal of Fourier Analysis and Applications 11, no. 4 (August 2005): 459–70. http://dx.doi.org/10.1007/s00041-005-4074-1.

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5

Ciprian Demeter and Christoph Thiele. "On the two-dimensional bilinear Hilbert transform." American Journal of Mathematics 132, no. 1 (2010): 201–56. http://dx.doi.org/10.1353/ajm.0.0101.

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Bilyk, Dmitriy, and Loukas Grafakos. "Distributional estimates for the bilinear Hilbert transform." Journal of Geometric Analysis 16, no. 4 (December 2006): 563–84. http://dx.doi.org/10.1007/bf02922131.

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Di Plinio, Francesco, and Christoph Thiele. "Endpoint bounds for the bilinear Hilbert transform." Transactions of the American Mathematical Society 368, no. 6 (November 20, 2015): 3931–72. http://dx.doi.org/10.1090/tran/6548.

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Lacey, M., and C. Thiele. "Lp estimates for the bilinear Hilbert transform." Proceedings of the National Academy of Sciences 94, no. 1 (January 7, 1997): 33–35. http://dx.doi.org/10.1073/pnas.94.1.33.

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Amenta, Alex, and Gennady Uraltsev. "The bilinear Hilbert transform in UMD spaces." Mathematische Annalen 378, no. 3-4 (August 5, 2020): 1129–221. http://dx.doi.org/10.1007/s00208-020-02052-y.

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Abstract We prove $$L^p$$ L p -bounds for the bilinear Hilbert transform acting on functions valued in intermediate UMD spaces. Such bounds were previously unknown for UMD spaces that are not Banach lattices. Our proof relies on bounds on embeddings from Bochner spaces $$L^p(\mathbb {R};X)$$ L p ( R ; X ) into outer Lebesgue spaces on the time-frequency-scale space $$\mathbb {R}^3_+$$ R + 3 .
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Bucˇkovska, A. L., and S. Pilipovic´. "An Extension of Bilinear Hilbert Transform to Distributions." Integral Transforms and Special Functions 13, no. 1 (January 2002): 1–15. http://dx.doi.org/10.1080/10652460212891.

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Dissertations / Theses on the topic "Bilinear Hilbert transform"

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Li, Xiaochun. "Uniform bounds for the bilinear Hilbert transforms /." free to MU campus, to others for purchase, 2001. http://wwwlib.umi.com/cr/mo/fullcit?p3025634.

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Oliveira, Filho Itamar Sales de. "Time-frequency analysis : The bilinear Hilbert transform and the Carleson theorem." reponame:Repositório Institucional da UFC, 2016. http://www.repositorio.ufc.br/handle/riufc/18888.

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OLIVEIRA FILHO, Itamar Sales de. Time-frequency analysis : the bilinear Hilbert transform and the Carleson theorem. 2016. 109 f. Dissertação (Mestrado em Matemática em Rede Nacional) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2016.
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In 1966, Lennart Carleson proved that the Fourier series of a periodic function, square integrable over a fundamental domain of the real line converges to the same function almost everywhere. This result was revisited years later by Charles Fe erman (1973) and by Lacey and Thiele (2000). It is studied here Lacey and Thiele's work, where they approached the problem through time-frequency analysis. This proof was inspired in a previous work of theirs, where they establish boundedness for the bilinear Hilbert transform in Lebesgue spaces. The study of boundedness for this operator started with the attempts to establish boundedness for the first Calderon's commutator. Also through time-frequency analysis, it will be studied one of the works of Lacey and Thiele about the bilinear Hilbert transform.
Em 1966, Lennart Carleson provou que a série de Fourier de uma função periódica, quadrado-integrável em um domínio fundamental na reta converge para a prápria função em quase todo ponto. Esse resultado foi revisitado alguns anos depois por Charles Fefferman (1973) e por Lacey e Thiele (2000). É estudado aqui o trabalho desses ultimos, onde o problema é abordado através de análise de tempo e frequência. Essa demonstração foi inspirada em um trabalho anterior dos mesmos autores em que estabelecem limitação para a transformada de Hilbert bilinear em espaços de Lebesgue. O estudo da limitação desse operador começou com as tentativas de estabelecer limitação para o primeiro comutador de Calderón. Também sob o ponto de vista da análise de tempo e frequência, será estudado um dos trabalhos de Lacey e Thiele sobre a transformada de Hilbert bilinear.
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Conference papers on the topic "Bilinear Hilbert transform"

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Yan, Guirong, Kai Zhao, Chen Fang, and Ruoqiang Feng. "Identification of Breathing Fatigue Cracks in Nonlinear Structures." In ASME 2014 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/smasis2014-7638.

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Fatigue cracks often occur in structural components due to dynamic loadings acting on them, such as wind loads and ground motion. If the static deflection due to dead loads is smaller than the vibration amplitude caused by dynamic loadings, these fatigue cracks alternately open and close with time, exhibiting a breathing-like behavior. This type of crack leads to a smaller change in structural dynamic characteristics than open cracks, and thus it is more difficult to be detected. If undetected timely, these fatigue cracks may lead to a catastrophic failure of the overall structure. Considering that breathing cracks introduce bilinearity into the structure, the present authors first developed a simple and efficient system identification method for bilinear systems by separating the global responses into two parts and performing Fourier transform on each set of separated data [1]. By applying this method, the natural frequency of each stiffness region can be identified. Then, breathing fatigue cracks can be detected by looking for the difference in the identified natural frequency between stiffness regions [1]. That approach is only applicable to the cases where the intact structure is linear. This study is to extend the approach in [1] to the cases when the intact structure is nonlinear, e.g., a structure with large displacements (geometrical nonlinearity). Once breathing cracks occur, there will exist both bilinearity (caused by breathing cracks) and cubic nonlinearity (caused by large displacements). To detect fatigue cracks in this case, Hilbert transform is proposed to be employed to process the separated data, instead of employing Fourier transform as in [1]. This approach has been successfully validated by numerical simulations.
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