The Experts below are selected from a list of 21168 Experts worldwide ranked by ideXlab platform
Jose Maria Martell - One of the best experts on this subject based on the ideXlab platform.
-
limited range multilinear extrapolation with applications to the bilinear Hilbert Transform
Mathematische Annalen, 2018Co-Authors: David Cruzuribe, Jose Maria MartellAbstract:We prove a limited range, off-diagonal extrapolation theorem that generalizes a number of results in the theory of Rubio de Francia extrapolation, and use this to prove a limited range, multilinear extrapolation theorem. We give two applications of this result to the bilinear Hilbert Transform. First, we give sufficient conditions on a pair of weights $$w_1,\,w_2$$ for the bilinear Hilbert Transform to satisfy weighted norm inequalities of the form $$\begin{aligned} BH : L^{p_1}\left( w_1^{p_1}\right) \times L^{p_2}\left( w_2^{p_2}\right) \longrightarrow L^p(w^p), \end{aligned}$$ where $$w=w_1w_2$$ and $$\frac{1}{p}=\frac{1}{p_1}+\frac{1}{p_2}<\frac{3}{2}$$ . This improves the recent results of Culiuc et al. by increasing the families of weights for which this inequality holds and by pushing the lower bound on p from 1 down to $$\frac{2}{3}$$ , the critical index from the unweighted theory of the bilinear Hilbert Transform. Second, as an easy consequence of our method we obtain that the bilinear Hilbert Transform satisfies some vector-valued inequalities with Muckenhoupt weights. This reproves and generalizes some of the vector-valued estimates obtained by Benea and Muscalu in the unweighted case. We also generalize recent results of Carando, et al. on Marcinkiewicz-Zygmund estimates for multilinear Calderon-Zygmund operators.
-
limited range multilinear extrapolation with applications to the bilinear Hilbert Transform
arXiv: Classical Analysis and ODEs, 2017Co-Authors: David Cruzuribe, Jose Maria MartellAbstract:We prove a limited range, off-diagonal extrapolation theorem that generalizes a number of results in the theory of Rubio de Francia extrapolation, and use this to prove a limited range, multilinear extrapolation theorem. We give two applications of this result to the bilinear Hilbert Transform. First, we give sufficient conditions on a pair of weights $w_1,\,w_2$ for the bilinear Hilbert Transform to satisfy weighted norm inequalities of the form \[ BH : L^{p_1}(w_1^{p_1}) \times L^{p_2}(w_2^{p_2}) \longrightarrow L^p(w^p), \] where $w=w_1w_2$ and $\frac{1}{p}=\frac{1}{p_1}+\frac{1}{p_2}<\frac{3}{2}$. This improves the recent results of Culiuc et al. by increasing the families of weights for which this inequality holds and by pushing the lower bound on $p$ from $1$ down to $\frac{2}{3}$, the critical index from the unweighted theory of the bilinear Hilbert Transform. We also prove that for the same exponents and the same weights, the bilinear Hilbert Transform satisfies vector-valued inequalities. This improves work of Benea and Muscalu who proved unweighted vector-valued inequalities but with restrictions on the possible values of $p_i$ in terms of the associated $\ell^r$ spaces. We also generalize recent results of Carando, et al. on Marcinkiewicz-Zygmund estimates for multilinear Calder\'on-Zygmund operators.
Huseyin Ozkaramanli - One of the best experts on this subject based on the ideXlab platform.
-
Hilbert Transform pairs of biorthogonal wavelet bases
IEEE Transactions on Signal Processing, 2006Co-Authors: Huseyin OzkaramanliAbstract:The forming of Hilbert Transform pairs of biorthogonal wavelet bases of two-band filter banks is studied in this paper. We first derive necessary and sufficient conditions on the scaling filters that render two Hilbert Transform pairs: one decomposition pair and one reconstruction pair. We show that the Hilbert Transform pairs are achieved if and only if the decomposition scaling filter of one filter bank is half-sample delayed from that of the other filter bank; and the reconstruction scaling filter of the former is half-sample advanced from that of the latter. Hilbert Transform pairs of wavelet bases are also characterized by equivalent relationships on the wavelet filters and the scaling functions associated with the two filter banks. An illustrative example is provided.
Michael Feldman - One of the best experts on this subject based on the ideXlab platform.
-
a signal decomposition or lowpass filtering with Hilbert Transform
Mechanical Systems and Signal Processing, 2011Co-Authors: Michael FeldmanAbstract:Abstract Recently, Chen and Wang discovered an explicit formula that makes use of the Hilbert Transform for accurate decomposition of a lower harmonic from a signal composition. This letter presents another proof with a new interpretation for the formula using the Bedrosian identity for overlapping signals. This new and simpler proof is based only on the Hilbert Transform and does not involve presentation of the Fourier Transform. As a result the discovered formula is introduced as a lowpass filter suitable for non-stationary signals.
-
Hilbert Transform in vibration analysis
Mechanical Systems and Signal Processing, 2011Co-Authors: Michael FeldmanAbstract:This paper is a tutorial on Hilbert Transform applications to mechanical vibration. The approach is accessible to non-stationary and nonlinear vibration application in the time domain. It thrives on a large number of examples devoted to illustrating key concepts on actual mechanical signals and demonstrating how the Hilbert Transform can be taken advantage of in machine diagnostics, identification of mechanical systems and decomposition of signal components.
David Cruzuribe - One of the best experts on this subject based on the ideXlab platform.
-
limited range multilinear extrapolation with applications to the bilinear Hilbert Transform
Mathematische Annalen, 2018Co-Authors: David Cruzuribe, Jose Maria MartellAbstract:We prove a limited range, off-diagonal extrapolation theorem that generalizes a number of results in the theory of Rubio de Francia extrapolation, and use this to prove a limited range, multilinear extrapolation theorem. We give two applications of this result to the bilinear Hilbert Transform. First, we give sufficient conditions on a pair of weights $$w_1,\,w_2$$ for the bilinear Hilbert Transform to satisfy weighted norm inequalities of the form $$\begin{aligned} BH : L^{p_1}\left( w_1^{p_1}\right) \times L^{p_2}\left( w_2^{p_2}\right) \longrightarrow L^p(w^p), \end{aligned}$$ where $$w=w_1w_2$$ and $$\frac{1}{p}=\frac{1}{p_1}+\frac{1}{p_2}<\frac{3}{2}$$ . This improves the recent results of Culiuc et al. by increasing the families of weights for which this inequality holds and by pushing the lower bound on p from 1 down to $$\frac{2}{3}$$ , the critical index from the unweighted theory of the bilinear Hilbert Transform. Second, as an easy consequence of our method we obtain that the bilinear Hilbert Transform satisfies some vector-valued inequalities with Muckenhoupt weights. This reproves and generalizes some of the vector-valued estimates obtained by Benea and Muscalu in the unweighted case. We also generalize recent results of Carando, et al. on Marcinkiewicz-Zygmund estimates for multilinear Calderon-Zygmund operators.
-
limited range multilinear extrapolation with applications to the bilinear Hilbert Transform
arXiv: Classical Analysis and ODEs, 2017Co-Authors: David Cruzuribe, Jose Maria MartellAbstract:We prove a limited range, off-diagonal extrapolation theorem that generalizes a number of results in the theory of Rubio de Francia extrapolation, and use this to prove a limited range, multilinear extrapolation theorem. We give two applications of this result to the bilinear Hilbert Transform. First, we give sufficient conditions on a pair of weights $w_1,\,w_2$ for the bilinear Hilbert Transform to satisfy weighted norm inequalities of the form \[ BH : L^{p_1}(w_1^{p_1}) \times L^{p_2}(w_2^{p_2}) \longrightarrow L^p(w^p), \] where $w=w_1w_2$ and $\frac{1}{p}=\frac{1}{p_1}+\frac{1}{p_2}<\frac{3}{2}$. This improves the recent results of Culiuc et al. by increasing the families of weights for which this inequality holds and by pushing the lower bound on $p$ from $1$ down to $\frac{2}{3}$, the critical index from the unweighted theory of the bilinear Hilbert Transform. We also prove that for the same exponents and the same weights, the bilinear Hilbert Transform satisfies vector-valued inequalities. This improves work of Benea and Muscalu who proved unweighted vector-valued inequalities but with restrictions on the possible values of $p_i$ in terms of the associated $\ell^r$ spaces. We also generalize recent results of Carando, et al. on Marcinkiewicz-Zygmund estimates for multilinear Calder\'on-Zygmund operators.
S.a. Scott - One of the best experts on this subject based on the ideXlab platform.
-
Interpolation/extrapolation of frequency domain responses using the Hilbert Transform
IEEE Transactions on Microwave Theory and Techniques, 1996Co-Authors: S.m. Narayana, Vincent C. Vannicola, Tapan K. Sarkar, Raviraj S Adve, Michael C Wicks, S.a. ScottAbstract:The Hilbert Transform relates the real and the imaginary parts of the transfer function of a causal system. The objective of this paper is to illustrate how the Hilbert Transform relationship can be utilized to interpolate/extrapolate measured frequency domain responses of devices. Sample numerical examples are presented to illustrate the efficacy of this method.