Edit Profile (opens in new tab) Qian, Tao Compute Distance To: Compute Author ID: qian.tao Published as: Qian, Tao; Qian, T. Homepage: http://www.fst.umac.mo/en/staff/fsttq.html External Links: GND Documents Indexed: 227 Publications since 1984, including 1 Book 4 Contributions as Editor Reviewing Activity: 3 Reviews Co-Authors: 117 Co-Authors with 197 Joint Publications 4,298 Co-Co-Authors all top 5 Co-Authors 32 single-authored 24 Dang, Pei 19 Chen, Qiuhui 16 Deng, Guantie 15 Yang, Yan 14 Mai, Weixiong 10 Zhang, Liming 9 Kou, Kit-Ian 9 Tan, Lihui 9 Wang, Jinxun 8 Sommen, Franciscus 7 Mi, Wen 6 Li, Haichou 6 Li, Pengtao 6 Sabadini, Irene 6 Wang, Yanbo 5 Gaudry, Garth Ian 5 Li, Luoqing 5 Li, Youfa 5 McIntosh, Alan 5 Qu, Wei 5 Yang, Qixiang 4 Chen, Xingdi 4 Colombo, Fabrizio 4 Fei, Minggang 4 Ku, Min 4 Li, Shuang 4 Zhong, Tongde 3 Alpay, Daniel Aron 3 Baratchart, Laurent 3 Dong, Baohua 3 Du, Zhihua 3 Gao, You 3 Long, Rulin 3 Mo, Yan 3 Mourão, José 3 Nunes, João Pedro Vidal 3 Peng, Lizhong 2 Cowling, Michael G. 2 Du, Jinyuan 2 Fu, Wenyuan 2 Gong, Yafang 2 Huang, Yun 2 Ji, Xinhua 2 Kwan, Chiman 2 Li, Chun 2 Li, Hong 2 Li, Xingmin 2 Li, Yanting 2 Ren, Guangbin 2 Rodino, Luigi 2 Schulze, Bert-Wolfgang 2 Wang, Jianzhong 2 Wang, Xiaoyin 2 Wang, Yi 2 Wu, Hio Tong 2 Xu, Roger 2 Xu, Yuesheng 2 Zhang, Yanhui 1 Axelsson, Andreas 1 Pinheiro de Castro, Luís Filipe 1 Chang, Der-Chen E. 1 Chen, Hongda 1 Chen, Jiecheng 1 Chen, Luping 1 Chen, Min 1 Chevillard, Sylvain 1 Chui, Charles Kam-tai 1 De Martino, Antonino 1 Delanghe, Richard 1 Fujiwara, Hiroshi 1 Guo, Yuanyuan 1 Hempfling, Thomas 1 Ho, Io-Tong 1 Hong, Wei 1 Huang, Yong 1 Jin, Ming 1 Kähler, Uwe 1 Kirwin, William D. 1 Lee, Weijen 1 Leong, Ieng Tak 1 Leong, Iengtak 1 Li, Dengfeng 1 Li, Yuan 1 Li, Zhixiong 1 Liu, Dangzheng 1 Liu, Hua 1 Liu, Shuang 1 Lv, Jianhao 1 Lyu, Xiaojing 1 Peetre, Jaak 1 Peña Peña, Dixan 1 Rao, Hangmei 1 Ren, Zhubing 1 Saitoh, Saburou 1 Sheeley, Joseph 1 Sjogren, Peter 1 Sprößig, Wolfgang 1 Stessin, Michael I. 1 Tan, Chunyu 1 Wan, Feng ...and 17 more Co-Authors all top 5 Serials 21 Mathematical Methods in the Applied Sciences 17 Complex Variables and Elliptic Equations 12 Journal of Mathematical Analysis and Applications 12 Advances in Applied Clifford Algebras 11 International Journal of Wavelets, Multiresolution and Information Processing 11 Complex Analysis and Operator Theory 6 Acta Mathematica Scientia. Series B. (English Edition) 5 Applied Mathematics and Computation 5 Journal of Functional Analysis 5 The Journal of Fourier Analysis and Applications 5 Science China. Mathematics 4 Applicable Analysis 4 Chinese Annals of Mathematics. Series B 3 Journal of Mathematical Physics 3 Arkiv för Matematik 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Automatica 3 Journal of Differential Equations 3 Science in China. Series A 3 IEEE Transactions on Signal Processing 2 Computers & Mathematics with Applications 2 Studia Mathematica 2 Journal of Geometry and Physics 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Proceedings of the American Mathematical Society 2 Transactions of the American Mathematical Society 2 Zeitschrift für Analysis und ihre Anwendungen 2 Complex Variables. Theory and Application 2 Physica D 2 Journal of the Australian Mathematical Society. Series A 2 Scientia Sinica. Series A 2 Applied and Computational Harmonic Analysis 2 Advances in Computational Mathematics 2 Taiwanese Journal of Mathematics 2 Scientia Sinica. Mathematica 2 Trends in Mathematics 1 Journal of the Franklin Institute 1 Acta Mathematica Sinica 1 Canadian Mathematical Bulletin 1 Colloquium Mathematicum 1 IEEE Transactions on Automatic Control 1 Journal of Approximation Theory 1 Journal of Computational and Applied Mathematics 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Monatshefte für Mathematik 1 Results in Mathematics 1 Journal of Operator Theory 1 Systems & Control Letters 1 Advances in Mathematics 1 Approximation Theory and its Applications 1 Revista Matemática Iberoamericana 1 Applied Mathematics Letters 1 Journal of Integral Equations and Applications 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 The Journal of Geometric Analysis 1 Kexue Tongbao 1 Acta Mathematica Sinica. New Series 1 Applied Mathematics. Series B (English Edition) 1 Methods and Applications of Analysis 1 Abstract and Applied Analysis 1 Acta Mathematica Sinica. English Series 1 IEEE Transactions on Image Processing 1 Nonlinear Analysis. Real World Applications 1 Journal of the Australian Mathematical Society 1 Acta Mathematica Scientia. Series A. (Chinese Edition) 1 Communications on Pure and Applied Analysis 1 Chinese Journal of Contemporary Mathematics 1 Computational Methods and Function Theory 1 Analysis and Applications (Singapore) 1 Boundary Value Problems 1 Frontiers of Mathematics in China 1 Journal of Pseudo-Differential Operators and Applications 1 Springer Proceedings in Mathematics & Statistics 1 International Journal of Systems Science. Principles and Applications of Systems and Integration all top 5 Fields 106 Functions of a complex variable (30-XX) 103 Harmonic analysis on Euclidean spaces (42-XX) 40 Information and communication theory, circuits (94-XX) 30 Several complex variables and analytic spaces (32-XX) 27 Functional analysis (46-XX) 24 Approximations and expansions (41-XX) 20 Operator theory (47-XX) 18 Numerical analysis (65-XX) 15 Partial differential equations (35-XX) 14 Potential theory (31-XX) 12 Integral transforms, operational calculus (44-XX) 11 Systems theory; control (93-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 7 Probability theory and stochastic processes (60-XX) 6 Integral equations (45-XX) 5 Statistics (62-XX) 4 General and overarching topics; collections (00-XX) 4 Quantum theory (81-XX) 4 Biology and other natural sciences (92-XX) 3 Abstract harmonic analysis (43-XX) 3 Computer science (68-XX) 2 Number theory (11-XX) 2 Measure and integration (28-XX) 2 Special functions (33-XX) 1 Nonassociative rings and algebras (17-XX) 1 Real functions (26-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Fluid mechanics (76-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 167 Publications have been cited 1,536 times in 538 Documents Cited by ▼ Year ▼ Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces. Zbl 0817.42008Li, Chun; McIntosh, Alan; Qian, Tao 66 1994 Adaptive Fourier series—a variation of greedy algorithm. Zbl 1214.30047Qian, Tao; Wang, Yan-Bo 59 2011 Analytic unit quadrature signals with nonlinear phase. Zbl 1070.94504Qian, Tao; Chen, Qiuhui; Li, Luoqing 49 2005 Characterization of boundary values of functions in Hardy spaces with applications in signal analysis. Zbl 1086.30035Qian, Tao 48 2005 Mono-components for decomposition of signals. Zbl 1104.94005Qian, Tao 38 2006 Generalization of Fueter’s result to \(\mathbb{R}^{n+1}\). Zbl 0909.30036Qian, Tao 37 1997 Intrinsic mono-component decomposition of functions: an advance of Fourier theory. Zbl 1188.42001Qian, Tao 34 2010 Singular integrals on star-shaped Lipschitz surfaces in the quaternionic space. Zbl 0921.42012Qian, Tao 32 1998 Frequency-domain identification: An algorithm based on an adaptive rational orthogonal system. Zbl 1244.93038Mi, Wen; Qian, Tao 29 2012 Generalizations of Fueter’s theorem. Zbl 1079.30066Kou, K. I.; Qian, T.; Sommen, F. 28 2002 Fourier spectrum characterization of Hardy spaces and applications. Zbl 1169.42003Qian, Tao; Xu, Yuesheng; Yan, Dunyan; Yan, Lixin; Yu, Bo 27 2009 Hardy-Sobolev spaces decomposition in signal analysis. Zbl 1211.30061Dang, Pei; Qian, Tao; You, Zhong 26 2011 A fast adaptive model reduction method based on Takenaka-Malmquist systems. Zbl 1256.93029Mi, Wen; Qian, Tao; Wan, Feng 25 2012 Boundary derivatives of the phases of inner and outer functions and applications. Zbl 1173.31001Qian, Tao 24 2009 Algorithm of adaptive Fourier decomposition. Zbl 1393.94142Qian, Tao; Zhang, Liming; Li, Zhixiong 24 2011 Fourier analysis on starlike Lipschitz surfaces. Zbl 0991.42009Qian, Tao 23 2001 Analytic phase derivatives, all-pass filters and signals of minimum phase. Zbl 1392.94170Dang, Pei; Qian, Tao 22 2011 Analytic signals and harmonic measures. Zbl 1082.94006Qian, Tao 22 2006 Optimal approximation by Blaschke forms. Zbl 1259.41021Qian, Tao; Wegert, Elias 21 2013 The Paley-Wiener theorem in \(\mathbb{R}^n\) with the Clifford analysis setting. Zbl 1015.42013Kou, Kit-Ian; Qian, Tao 20 2002 Two families of unit analytic signals with nonlinear phase. Zbl 1104.94004Chen, Qiuhui; Li, Luoqing; Qian, Tao 20 2006 A tighter uncertainty principle for linear canonical transform in terms of phase derivative. Zbl 1393.94205Dang, Pei; Deng, Guan-Tie; Qian, Tao 20 2013 A sharper uncertainty principle. Zbl 1284.42019Dang, Pei; Deng, Guan-Tie; Qian, Tao 19 2013 Stability of frames generated by nonlinear Fourier atoms. Zbl 1086.42018Chen, Qiuhui; Li, Luoqing; Qian, Tao 19 2005 Orthonormal bases with nonlinear phases. Zbl 1213.42126Qian, Tao; Wang, Rui; Xu, Yuesheng; Zhang, Haizhang 19 2010 Deriving harmonic functions in higher dimensional spaces. Zbl 1052.30055Qian, T.; Sommen, F. 17 2003 Conformal transformations and Hardy spaces arising in Clifford analysis. Zbl 0856.30037Qian, Tao; Ryan, John 16 1996 An alternative proof of Fueter’s theorem. Zbl 1117.30039Peña Peña, Dixan; Qian, Tao; Sommen, Frank 16 2006 Convolution singular integral operators on Lipschitz curves. Zbl 0791.42012McIntosh, Alan; Qian, Tao 16 1991 Adaptive Fourier decomposition of functions in quaternionic Hardy spaces. Zbl 1254.30086Qian, Tao; Sprößig, Wolfgang; Wang, Jinxun 16 2012 Two integral operators in Clifford analysis. Zbl 1182.30082Gong, Yafang; Leong, Ieng Tak; Qian, Tao 16 2009 The \(H^{\infty}\) functional calculus based on the \(S\)-spectrum for quaternionic operators and for \(n\)-tuples of noncommuting operators. Zbl 1350.47017Alpay, Daniel; Colombo, Fabrizio; Qian, Tao; Sabadini, Irene 15 2016 Adaptive decomposition by weighted inner functions: a generalization of Fourier series. Zbl 1223.42006Qian, Tao; Tan, Li-Hui; Wang, Yan-Bo 15 2011 A martingale proof of \(L_ 2\) boundedness of Clifford-valued singular integrals. Zbl 0814.42009Gaudry, G. I.; Long, R.; Qian, T. 14 1993 Two-dimensional adaptive Fourier decomposition. Zbl 1347.42047Qian, Tao 14 2016 Cyclic AFD algorithm for the best rational approximation. Zbl 1287.42018Qian, Tao 14 2014 Structure of solutions of polynomial Dirac equations in Clifford analysis. Zbl 1054.30049Gong, Y. F.; Qian, T.; Du, D. Y. 14 2004 Hilbert transforms on the sphere with the Clifford algebra setting. Zbl 1182.30092Qian, Tao; Yang, Yan 13 2009 Tighter uncertainty principles based on quaternion Fourier transform. Zbl 1338.42013Yang, Yan; Dang, Pei; Qian, Tao 13 2016 Möbius covariance of iterated Dirac operators. Zbl 1043.31500Peetre, Jaak; Qian, Tao 12 1994 Singular integrals associated to the Laplacian on the affine group \(ax+b\). Zbl 0776.43003Gaudry, G. I.; Qian, T.; Sjögren, P. 12 1992 Rational orthogonal systems are Schauder bases. Zbl 1306.46023Qian, Tao; Chen, Qiuhui; Tan, Lihui 12 2014 Comparison of adaptive mono-component decompositions. Zbl 1270.94041Qian, Tao; Li, Hong; Stessin, Michael 12 2013 Singular integrals with holomorphic kernels and Fourier multipliers on star-shaped closed Lipschitz curves. Zbl 0924.42012Qian, Tao 12 1997 Schwarz lemma in Euclidean spaces. Zbl 1105.30039Yang, Yan; Qian, Tao 11 2006 Hardy-Sobolev derivatives of phase and amplitude, and their applications. Zbl 1256.42012Dang, Pei; Qian, Tao; Yang, Yan 11 2012 Mono-components vs IMFs in signal decomposition. Zbl 1145.94374Qian, Tao; Zhang, Liming; Li, Hong 11 2008 Adaptative decomposition: the case of the Drury-Arveson space. Zbl 06829778Alpay, Daniel; Colombo, Fabrizio; Qian, Tao; Sabadini, Irene 11 2017 Adaptive orthonormal systems for matrix-valued functions. Zbl 1370.47011Alpay, Daniel; Colombo, Fabrizio; Qian, Tao; Sabadini, Irene 11 2017 Cauchy integrals on Lipschitz surfaces in octonionic space. Zbl 1151.30038Li, Xing Min; Peng, Li Zhong; Qian, Tao 11 2008 On backward shift algorithm for estimating poles of systems. Zbl 1296.93068Mi, Wen; Qian, Tao 10 2014 Rational approximation of functions in Hardy spaces. Zbl 1353.30032Deng, Guantie; Qian, Tao 10 2016 \(L^p\) polyharmonic Dirichlet problems in regular domains. II: The upper half plane. Zbl 1256.31002Du, Zhihua; Qian, Tao; Wang, Jinxun 10 2012 Extending coherent state transforms to Clifford analysis. Zbl 1349.81088Kirwin, William D.; Mourão, José; Nunes, João P.; Qian, Tao 10 2016 Phase derivative of monogenic signals in higher dimensional spaces. Zbl 1275.30027Yang, Yan; Qian, Tao; Sommen, Frank 10 2012 Adaptive decomposition of functions into pieces of non-negative instantaneous frequencies. Zbl 1200.94026Qian, Tao; Ho, I. T.; Leong, I. T.; Wang, Yanbo 9 2010 The Paley-Wiener theorem in the non-commutative and non-associative octonions. Zbl 1176.42019Li, XingMin; Peng, LiZhong; Qian, Tao 9 2009 Remarks on adaptive Fourier decomposition. Zbl 1267.42006Qian, Tao; Wang, Yanbo 9 2013 Coherent state transforms and the Weyl equation in Clifford analysis. Zbl 1355.81076Mourão, José; Nunes, João P.; Qian, Tao 9 2017 Estimation of hyperbolically partial derivatives of \(\rho\)-harmonic quasiconformal mappings and its applications. Zbl 1317.30025Chen, Xingdi; Qian, Tao 8 2015 Hilbert transforms and the Cauchy integral in Euclidean space. Zbl 1168.45001Axelsson, Andreas; Kou, Kit Ian; Qian, Tao 8 2009 Sampling theorem and multi-scale spectrum based on non-linear Fourier atoms. Zbl 1171.94331Chen, Qiuhui; Qian, Tao 8 2009 Fourier multipliers on Lipschitz curves. Zbl 0766.42005McIntosh, Alan; Qian, Tao 7 1992 Boundedness of singular integral operators with holomorphic kernels on star-shaped closed Lipschitz curves. Zbl 0860.42013Gaudry, Garth; Qian, Tao; Wang, Silei 7 1996 Fueter mapping theorem in hypercomplex analysis. Zbl 1330.30005Qian, Tao 7 2015 Matching pursuits among shifted Cauchy kernels in higher-dimensional spaces. Zbl 1313.30164Qian, Tao; Wang, Jinxun; Yang, Yan 7 2014 Singular integrals and Fourier theory on Lipschitz boundaries. Zbl 1435.47001Qian, Tao; Li, Pengtao 7 2019 Fourier spectrum characterizations of \(H^{p}\) spaces on tubes over cones for \(1\leq p \leq \infty \). Zbl 06909439Li, Hai-Chou; Deng, Guan-Tie; Qian, Tao 7 2018 An enhancement algorithm for cyclic adaptive Fourier decomposition. Zbl 1426.41012Qian, Tao; Wang, Jianzhong; Mai, Weixiong 7 2019 2D partial unwinding – a novel non-linear phase decomposition of images. Zbl 07123013Li, Yanting; Zhang, Liming; Qian, Tao 7 2019 Backward shift invariant subspaces with applications to band preserving and phase retrieval problems. Zbl 1381.47006Qian, Tao; Tan, Lihui 7 2016 Aveiro method in reproducing kernel Hilbert spaces under complete dictionary. Zbl 1382.30005Mai, Weixiong; Qian, Tao 7 2017 Transient time-frequency distribution based on mono-component decompositions. Zbl 1316.94025Dang, Pei; Qian, Tao; Guo, Yuan Yuan 7 2013 Support vector machine adapted Tikhonov regularization method to solve Dirichlet problem. Zbl 1337.65172Mo, Yan; Qian, Tao 6 2014 Uncertainty principle and phase-amplitude analysis of signals on the unit sphere. Zbl 1386.94025Dang, Pei; Qian, Tao; Chen, Qiuhui 6 2017 Hardy-Hodge decomposition of vector fields in \(\mathbb {R}^n\). Zbl 1385.42018Baratchart, Laurent; Dang, Pei; Qian, Tao 6 2018 On the inversion of Fueter’s theorem. Zbl 1348.30027Dong, Baohua; Kou, Kit Ian; Qian, Tao; Sabadini, Irene 6 2016 Mathematical theory of signal analysis vs. complex analysis method of harmonic analysis. Zbl 1299.42011Qian, Tao; Zhang, Liming 5 2013 Integral representations of a class of harmonic functions in the half space. Zbl 1329.35106Zhang, Yan Hui; Deng, Guan Tie; Qian, Tao 5 2016 Stronger uncertainty principles for hypercomplex signals. Zbl 1342.42006Yang, Yan; Dang, Pei; Qian, Tao 5 2015 Sparse representation in Szegő kernels through reproducing kernel Hilbert space theory with applications. Zbl 1320.93036Mo, Y.; Qian, T.; Mi, W. 5 2015 Approximation of monogenic functions by higher order Szegő kernels on the unit ball and half space. Zbl 1302.30068Wang, Jinxun; Qian, Tao 5 2014 Spaces of harmonic functions with boundary values in \(Q^{\alpha}_{p,q}\). Zbl 1307.42022Yang, Qixiang; Qian, Tao; Li, Pengtao 5 2014 A novel Fourier theory on nonlinear phases and applications. Zbl 1424.32016Qian, Tao 5 2018 Extra-strong uncertainty principles in relation to phase derivative for signals in Euclidean spaces. Zbl 1366.94092Dang, Pei; Qian, Tao; Yang, Yan 5 2016 Two-dimensional frequency-domain system identification. Zbl 07256186Wang, Xiaoyin; Qian, Tao; Leong, Iengtak; Gao, You 5 2020 The inverse Fueter mapping theorem for axially monogenic functions of degree \(k\). Zbl 1414.30050Dong, Baohua; Kou, Kit Ian; Qian, Tao; Sabadini, Irene 5 2019 Schwarz problems for poly-Hardy space on the unit ball. Zbl 1384.30009Kähler, Uwe; Ku, Min; Qian, Tao 5 2017 The AFD methods to compute Hilbert transform. Zbl 1325.42002Mo, Yan; Qian, Tao; Mai, Weixiong; Chen, Qiuhui 4 2015 Non-stretch mappings for a sharp estimate of the Beurling-Ahlfors operator. Zbl 1319.42010Chen, Xingdi; Qian, Tao 4 2014 Fixed trace {\(\beta\)}-Hermite ensembles: asymptotic eigenvalue density and the edge of the density. Zbl 1309.15056Zhou, Da-Sheng; Liu, Dang-Zheng; Qian, Tao 4 2010 \(L^{p}\) polyharmonic Dirichlet problems in regular domains. III: The unit ball. Zbl 1295.31020Du, Zhihua; Qian, Tao; Wang, Jinxun 4 2014 Space-frequency analysis in higher dimensions and applications. Zbl 1329.46038Yang, Yan; Dang, Pei; Qian, Tao 4 2015 Extracting outer function part from Hardy space function. Zbl 1395.30055Tan, LiHui; Qian, Tao 4 2017 Fourier spectrum of Clifford \(H^p\) spaces on \(\mathbb{R}_+^{n + 1}\) for \(1 \leq p \leq \infty \). Zbl 1432.42013Dang, Pei; Mai, Weixiong; Qian, Tao 4 2020 Hardy space decomposition of \(L^p\) on the unit circle: \(0 < p \leq 1\). Zbl 1342.30050Li, Hai-Chou; Deng, Guan-Tie; Qian, Tao 4 2016 Boundary value problems for periodic analytic functions. Zbl 1338.30027Dang, Pei; Du, Jinyuan; Qian, Tao 4 2015 The differential integral equations on smooth closed orientable manifolds. Zbl 0995.32004Qian, Tao; Zhong, Tongde 4 2001 Greedy algorithms and rational approximation in one and several variables. Zbl 1388.30063Baratchart, Laurent; Mai, Wei-Xiong; Qian, Tao 4 2016 On sets of zeroes of Clifford algebra-valued polynomials. Zbl 1240.30215Yang, Yan; Qian, Tao 4 2010 The Fourier type expansions on tubes. Zbl 1484.32008Mai, Weixiong; Qian, Tao 1 2022 The Poisson kernel and the Fourier transform of the slice monogenic Cauchy kernels. Zbl 1486.30133Colombo, Fabrizio; De Martino, Antonino; Qian, Tao; Sabadini, Irene 1 2022 Two-dimensional frequency-domain system identification. Zbl 07256186Wang, Xiaoyin; Qian, Tao; Leong, Iengtak; Gao, You 5 2020 Fourier spectrum of Clifford \(H^p\) spaces on \(\mathbb{R}_+^{n + 1}\) for \(1 \leq p \leq \infty \). Zbl 1432.42013Dang, Pei; Mai, Weixiong; Qian, Tao 4 2020 Reproducing kernel sparse representations in relation to operator equations. Zbl 1436.42006Qian, Tao 3 2020 A theory on non-constant frequency decompositions and applications. Zbl 1494.94015Chen, Qiuhui; Qian, Tao; Tan, Lihui 3 2020 AFD-based ILC designs in frequency domain for linear discrete-time systems. Zbl 1483.93161Fu, Wen-Yuan; Li, Xiao-Dong; Qian, Tao 1 2020 Singular integrals and Fourier theory on Lipschitz boundaries. Zbl 1435.47001Qian, Tao; Li, Pengtao 7 2019 An enhancement algorithm for cyclic adaptive Fourier decomposition. Zbl 1426.41012Qian, Tao; Wang, Jianzhong; Mai, Weixiong 7 2019 2D partial unwinding – a novel non-linear phase decomposition of images. Zbl 07123013Li, Yanting; Zhang, Liming; Qian, Tao 7 2019 The inverse Fueter mapping theorem for axially monogenic functions of degree \(k\). Zbl 1414.30050Dong, Baohua; Kou, Kit Ian; Qian, Tao; Sabadini, Irene 5 2019 A novel 2D partial unwinding adaptive Fourier decomposition method with application to frequency domain system identification. Zbl 1418.42008Li, Yanting; Qian, Tao 2 2019 Paley-Wiener-type theorem for analytic functions in tubular domains. Zbl 1427.32005Deng, Guan-Tie; Huang, Yun; Qian, Tao 1 2019 Fourier spectrum characterizations of \(H^{p}\) spaces on tubes over cones for \(1\leq p \leq \infty \). Zbl 06909439Li, Hai-Chou; Deng, Guan-Tie; Qian, Tao 7 2018 Hardy-Hodge decomposition of vector fields in \(\mathbb {R}^n\). Zbl 1385.42018Baratchart, Laurent; Dang, Pei; Qian, Tao 6 2018 A novel Fourier theory on nonlinear phases and applications. Zbl 1424.32016Qian, Tao 5 2018 Characterizations of mono-components: the Blaschke and starlike types. Zbl 1491.30007Qian, Tao; Tan, Lihui 3 2018 Rational approximation in Hardy spaces on strips. Zbl 1407.30017Mai, Weixiong; Qian, Tao 2 2018 Clifford coherent state transforms on spheres. Zbl 1431.81035Dang, Pei; Mourão, José; Nunes, João P.; Qian, Tao 2 2018 Wavelets and holomorphic functions. Zbl 1397.30041Qian, Tao; Yang, Qixiang 1 2018 Hilbert transformation and representation of the \(ax+b\) group. Zbl 1388.30047Dang, Pei; Liu, Hua; Qian, Tao 1 2018 Adaptative decomposition: the case of the Drury-Arveson space. Zbl 06829778Alpay, Daniel; Colombo, Fabrizio; Qian, Tao; Sabadini, Irene 11 2017 Adaptive orthonormal systems for matrix-valued functions. Zbl 1370.47011Alpay, Daniel; Colombo, Fabrizio; Qian, Tao; Sabadini, Irene 11 2017 Coherent state transforms and the Weyl equation in Clifford analysis. Zbl 1355.81076Mourão, José; Nunes, João P.; Qian, Tao 9 2017 Aveiro method in reproducing kernel Hilbert spaces under complete dictionary. Zbl 1382.30005Mai, Weixiong; Qian, Tao 7 2017 Uncertainty principle and phase-amplitude analysis of signals on the unit sphere. Zbl 1386.94025Dang, Pei; Qian, Tao; Chen, Qiuhui 6 2017 Schwarz problems for poly-Hardy space on the unit ball. Zbl 1384.30009Kähler, Uwe; Ku, Min; Qian, Tao 5 2017 Extracting outer function part from Hardy space function. Zbl 1395.30055Tan, LiHui; Qian, Tao 4 2017 Adaptive Fourier decomposition-based Dirac type time-frequency distribution. Zbl 1369.94331Zhang, Liming; Qian, Tao; Mai, Weixiong; Dang, Pei 3 2017 FFT formulations of adaptive Fourier decomposition. Zbl 1369.65184Gao, You; Ku, Min; Qian, Tao; Wang, Jianzhong 3 2017 Rational approximation of functions in Hardy spaces. Zbl 1382.30069Deng, Guantie; Li, Haichou; Qian, Tao 1 2017 A frame theory of Hardy spaces with the quaternionic and the Clifford algebra settings. Zbl 1376.42009Chen, Qiuhui; Dang, Pei; Qian, Tao 1 2017 The \(H^{\infty}\) functional calculus based on the \(S\)-spectrum for quaternionic operators and for \(n\)-tuples of noncommuting operators. Zbl 1350.47017Alpay, Daniel; Colombo, Fabrizio; Qian, Tao; Sabadini, Irene 15 2016 Two-dimensional adaptive Fourier decomposition. Zbl 1347.42047Qian, Tao 14 2016 Tighter uncertainty principles based on quaternion Fourier transform. Zbl 1338.42013Yang, Yan; Dang, Pei; Qian, Tao 13 2016 Rational approximation of functions in Hardy spaces. Zbl 1353.30032Deng, Guantie; Qian, Tao 10 2016 Extending coherent state transforms to Clifford analysis. Zbl 1349.81088Kirwin, William D.; Mourão, José; Nunes, João P.; Qian, Tao 10 2016 Backward shift invariant subspaces with applications to band preserving and phase retrieval problems. Zbl 1381.47006Qian, Tao; Tan, Lihui 7 2016 On the inversion of Fueter’s theorem. Zbl 1348.30027Dong, Baohua; Kou, Kit Ian; Qian, Tao; Sabadini, Irene 6 2016 Integral representations of a class of harmonic functions in the half space. Zbl 1329.35106Zhang, Yan Hui; Deng, Guan Tie; Qian, Tao 5 2016 Extra-strong uncertainty principles in relation to phase derivative for signals in Euclidean spaces. Zbl 1366.94092Dang, Pei; Qian, Tao; Yang, Yan 5 2016 Hardy space decomposition of \(L^p\) on the unit circle: \(0 < p \leq 1\). Zbl 1342.30050Li, Hai-Chou; Deng, Guan-Tie; Qian, Tao 4 2016 Greedy algorithms and rational approximation in one and several variables. Zbl 1388.30063Baratchart, Laurent; Mai, Wei-Xiong; Qian, Tao 4 2016 Consecutive minimum phase expansion of physically realizable signals with applications. Zbl 1332.30085Mai, Weixiong; Dang, Pei; Zhang, Liming; Qian, Tao 3 2016 Fefferman-Stein decomposition for \(Q\)-spaces and micro-local quantities. Zbl 1350.42043Yang, Qixiang; Qian, Tao; Li, Pengtao 3 2016 Basis pursuit for frequency-domain identification. Zbl 1382.93034Mi, Wen; Qian, Tao; Li, Shuang 3 2016 Minimax principle and lower bounds in \(H^2\)-rational approximation. Zbl 1361.30057Baratchart, Laurent; Chevillard, Sylvain; Qian, Tao 3 2016 Estimation of hyperbolically partial derivatives of \(\rho\)-harmonic quasiconformal mappings and its applications. Zbl 1317.30025Chen, Xingdi; Qian, Tao 8 2015 Fueter mapping theorem in hypercomplex analysis. Zbl 1330.30005Qian, Tao 7 2015 Stronger uncertainty principles for hypercomplex signals. Zbl 1342.42006Yang, Yan; Dang, Pei; Qian, Tao 5 2015 Sparse representation in Szegő kernels through reproducing kernel Hilbert space theory with applications. Zbl 1320.93036Mo, Y.; Qian, T.; Mi, W. 5 2015 The AFD methods to compute Hilbert transform. Zbl 1325.42002Mo, Yan; Qian, Tao; Mai, Weixiong; Chen, Qiuhui 4 2015 Space-frequency analysis in higher dimensions and applications. Zbl 1329.46038Yang, Yan; Dang, Pei; Qian, Tao 4 2015 Boundary value problems for periodic analytic functions. Zbl 1338.30027Dang, Pei; Du, Jinyuan; Qian, Tao 4 2015 Corner boundary value problems. Zbl 1327.35476Chang, Der-Chen; Qian, Tao; Schulze, Bert-Wolfgang 3 2015 New aspects of Beurling-Lax shift invariant subspaces. Zbl 1338.94021Tan, Lihui; Qian, Tao; Chen, Qiuhui 3 2015 A constructive proof of Beurling-Lax theorem. Zbl 1309.30045Chen, Qiuhui; Qian, Tao 2 2015 Order filtrations of the edge algebra. Zbl 1328.58025Lyu, Xiaojing; Qian, Tao; Schulze, B.-W. 2 2015 Cyclic AFD algorithm for the best rational approximation. Zbl 1287.42018Qian, Tao 14 2014 Rational orthogonal systems are Schauder bases. Zbl 1306.46023Qian, Tao; Chen, Qiuhui; Tan, Lihui 12 2014 On backward shift algorithm for estimating poles of systems. Zbl 1296.93068Mi, Wen; Qian, Tao 10 2014 Matching pursuits among shifted Cauchy kernels in higher-dimensional spaces. Zbl 1313.30164Qian, Tao; Wang, Jinxun; Yang, Yan 7 2014 Support vector machine adapted Tikhonov regularization method to solve Dirichlet problem. Zbl 1337.65172Mo, Yan; Qian, Tao 6 2014 Approximation of monogenic functions by higher order Szegő kernels on the unit ball and half space. Zbl 1302.30068Wang, Jinxun; Qian, Tao 5 2014 Spaces of harmonic functions with boundary values in \(Q^{\alpha}_{p,q}\). Zbl 1307.42022Yang, Qixiang; Qian, Tao; Li, Pengtao 5 2014 Non-stretch mappings for a sharp estimate of the Beurling-Ahlfors operator. Zbl 1319.42010Chen, Xingdi; Qian, Tao 4 2014 \(L^{p}\) polyharmonic Dirichlet problems in regular domains. III: The unit ball. Zbl 1295.31020Du, Zhihua; Qian, Tao; Wang, Jinxun 4 2014 How to catch smoothing properties and analyticity of functions by computers? Zbl 1328.65126Castro, L. P.; Fujiwara, H.; Qian, T.; Saitoh, S. 3 2014 Adaptive Fourier decompositions and rational approximations. I: Theory. Zbl 1304.65283Qian, Tao 3 2014 Sampling error analysis and some properties of non-bandlimited signals that are reconstructed by generalized sinc functions. Zbl 1290.94024Li, Youfa; Chen, Qiuhui; Qian, Tao; Wang, Yi 3 2014 Holomorphic approximation of \(L_2\)-functions on the unit sphere in \(\mathbb R^3\). Zbl 1312.30063De Schepper, Nele; Qian, Tao; Sommen, Frank; Wang, Jinxun 1 2014 Adaptive Fourier decomposition and rational approximation. II: Software system design and development. Zbl 1303.65113Zhang, Liming; Hong, Wei; Mai, Weixiong; Qian, Tao 1 2014 Optimal approximation by Blaschke forms. Zbl 1259.41021Qian, Tao; Wegert, Elias 21 2013 A tighter uncertainty principle for linear canonical transform in terms of phase derivative. Zbl 1393.94205Dang, Pei; Deng, Guan-Tie; Qian, Tao 20 2013 A sharper uncertainty principle. Zbl 1284.42019Dang, Pei; Deng, Guan-Tie; Qian, Tao 19 2013 Comparison of adaptive mono-component decompositions. Zbl 1270.94041Qian, Tao; Li, Hong; Stessin, Michael 12 2013 Remarks on adaptive Fourier decomposition. Zbl 1267.42006Qian, Tao; Wang, Yanbo 9 2013 Transient time-frequency distribution based on mono-component decompositions. Zbl 1316.94025Dang, Pei; Qian, Tao; Guo, Yuan Yuan 7 2013 Mathematical theory of signal analysis vs. complex analysis method of harmonic analysis. Zbl 1299.42011Qian, Tao; Zhang, Liming 5 2013 \(L^p\) polyharmonic Dirichlet problems in regular domains. IV: The upper-half space. Zbl 1288.31004Du, Zhihua; Qian, Tao; Wang, Jinxun 3 2013 Shannon-type sampling for multivariate non-bandlimited signals. Zbl 1283.94030Chen, Qiuhui; Qian, Tao; Li, Youfa 3 2013 Sufficient conditions for shift-invariant systems to be frames in \(L^2({\mathbb R^n})\). Zbl 1272.42020Li, Deng Feng; Qian, Tao 2 2013 Analytic sampling approximation by projection operator with application in decomposition of instantaneous frequency. Zbl 1279.41020Li, Youfa; Qian, Tao 2 2013 Micro-local structure and two kinds of wavelet characterizations about the generalized Hardy spaces. Zbl 1284.42048Yang, Qixiang; Qian, Tao 2 2013 Sparse reconstruction of Hardy signal and applications to time-frequency distribution. Zbl 1275.41017Qian, Tao; Li, Shuang; Mai, Weixiong 2 2013 Frequency-domain identification: An algorithm based on an adaptive rational orthogonal system. Zbl 1244.93038Mi, Wen; Qian, Tao 29 2012 A fast adaptive model reduction method based on Takenaka-Malmquist systems. Zbl 1256.93029Mi, Wen; Qian, Tao; Wan, Feng 25 2012 Adaptive Fourier decomposition of functions in quaternionic Hardy spaces. Zbl 1254.30086Qian, Tao; Sprößig, Wolfgang; Wang, Jinxun 16 2012 Hardy-Sobolev derivatives of phase and amplitude, and their applications. Zbl 1256.42012Dang, Pei; Qian, Tao; Yang, Yan 11 2012 \(L^p\) polyharmonic Dirichlet problems in regular domains. II: The upper half plane. Zbl 1256.31002Du, Zhihua; Qian, Tao; Wang, Jinxun 10 2012 Phase derivative of monogenic signals in higher dimensional spaces. Zbl 1275.30027Yang, Yan; Qian, Tao; Sommen, Frank 10 2012 Higher order boundary integral formula and integro-differential equation on Stein mainfolds. Zbl 1275.32005Chen, Lüping; Zhong, Tongde; Qian, Tao 2 2012 Some remarks on the boundary behaviors of functions in the monogenic Hardy spaces. Zbl 1257.30057Qian, Tao; Wang, Jinxun 1 2012 Adaptive Fourier series—a variation of greedy algorithm. Zbl 1214.30047Qian, Tao; Wang, Yan-Bo 59 2011 Hardy-Sobolev spaces decomposition in signal analysis. Zbl 1211.30061Dang, Pei; Qian, Tao; You, Zhong 26 2011 Algorithm of adaptive Fourier decomposition. Zbl 1393.94142Qian, Tao; Zhang, Liming; Li, Zhixiong 24 2011 Analytic phase derivatives, all-pass filters and signals of minimum phase. Zbl 1392.94170Dang, Pei; Qian, Tao 22 2011 Adaptive decomposition by weighted inner functions: a generalization of Fourier series. Zbl 1223.42006Qian, Tao; Tan, Li-Hui; Wang, Yan-Bo 15 2011 Zeroes of slice monogenic functions. Zbl 1220.30071Yang, Yan; Qian, Tao 2 2011 Zero-sets of Clifford analytic functions with real coefficients. Zbl 1249.30138Yang, Yan; Qian, Tao 1 2011 ...and 67 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 509 Authors 132 Qian, Tao 30 Colombo, Fabrizio 30 Sabadini, Irene 29 Dang, Pei 26 Chen, Qiuhui 23 Sommen, Franciscus 17 Deng, Guantie 16 Mai, Weixiong 15 Kähler, Uwe 15 Tan, Lihui 14 Li, Pingrun 14 Yang, Yan 13 Ku, Min 12 Li, Youfa 11 Cerejeiras, Paula 11 Kou, Kit-Ian 11 Kraußhar, Rolf Sören 11 Wang, Jinxun 10 Peña Peña, Dixan 10 Yang, Lihua 9 Li, Xingmin 9 Zhang, Liming 8 Alpay, Daniel Aron 8 Li, Luoqing 8 Ren, Guangbin 7 Gantner, Jonathan 7 Mi, Wen 7 Zhang, Haizhang 6 De Bie, Hendrik 6 Diki, Kamal 6 Fei, Minggang 6 Li, Pengtao 6 Pinton, Stefano 6 Vallarino, Maria 5 Axelsson, Andreas 5 Baratchart, Laurent 5 Bernstein, Swanhild 5 Brackx, Fred F. 5 Constales, Denis 5 Du, Zhihua 5 Fu, Yingxiong 5 Li, Haichou 5 Liao, Jianquan 5 Liu, Mingsheng 5 McIntosh, Alan 5 Peng, Lizhong 5 Perotti, Alessandro 5 Qu, Wei 5 Wang, Yanbo 4 Bahri, Mawardi 4 De Martino, Antonino 4 De Schepper, Hennie 4 Ding, Chao 4 Gu, Longfei 4 Huang, Chao 4 Kimsey, David Patrick 4 Li, Hong 4 Li, Shanshan 4 Qiao, Yuying 4 Schulze, Bert-Wolfgang 4 Sjogren, Peter 4 Wang, Daoshun 4 Wang, Yi 4 Wang, Yufeng 4 Zhang, Zhichao 3 Abdulhadi, Zayid 3 Ashino, Ryuichi 3 Auscher, Pascal 3 Bory Reyes, Juan 3 Chen, Luping 3 Coifman, Ronald Raphaël 3 Dong, Baohua 3 Gerhards, Christian 3 Ghanmi, Allal 3 González-Cervantes, José Óscar 3 Guo, Guoan 3 Han, Deguang 3 Jefferies, Brian R. F. 3 Li, Chun 3 Li, Shuang 3 Lin, Rongrong 3 Morais, João Pedro 3 Mourão, José 3 Nunes, João Pedro Vidal 3 Saitoh, Saburou 3 Walter, Raymond 3 Wang, Ying 3 Wen, Zhihong 3 Wu, Hau-Tieng 3 Yan, Dunyan 3 Yang, Qixiang 3 Yang, Shouzhi 3 Yuan, Hongfen 3 Zhang, Zhongxiang 2 Abreu-Blaya, Ricardo 2 Agarwal, Ravi P. 2 Ahmad, Owais 2 Ali, Rosihan Mohamed 2 Banouh, Hicham 2 Begehr, Heinrich ...and 409 more Authors all top 5 Cited in 129 Serials 48 Advances in Applied Clifford Algebras 39 Complex Variables and Elliptic Equations 34 International Journal of Wavelets, Multiresolution and Information Processing 33 Mathematical Methods in the Applied Sciences 29 Journal of Mathematical Analysis and Applications 28 Complex Analysis and Operator Theory 15 The Journal of Fourier Analysis and Applications 13 Applied Mathematics and Computation 12 Science China. Mathematics 11 Journal of Mathematical Physics 9 Journal of Functional Analysis 7 The Journal of Geometric Analysis 7 Acta Mathematica Sinica. 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New Series 1 Applicationes Mathematicae 1 Computational and Applied Mathematics 1 Journal of Difference Equations and Applications 1 Discrete and Continuous Dynamical Systems 1 Taiwanese Journal of Mathematics ...and 29 more Serials all top 5 Cited in 45 Fields 258 Functions of a complex variable (30-XX) 165 Harmonic analysis on Euclidean spaces (42-XX) 85 Information and communication theory, circuits (94-XX) 53 Operator theory (47-XX) 49 Numerical analysis (65-XX) 48 Functional analysis (46-XX) 46 Partial differential equations (35-XX) 40 Several complex variables and analytic spaces (32-XX) 35 Approximations and expansions (41-XX) 33 Integral transforms, operational calculus (44-XX) 29 Integral equations (45-XX) 28 Linear and multilinear algebra; matrix theory (15-XX) 27 Potential theory (31-XX) 21 Global analysis, analysis on manifolds (58-XX) 17 Abstract harmonic analysis (43-XX) 16 Quantum theory (81-XX) 14 Special functions (33-XX) 13 Systems theory; control (93-XX) 11 Statistics (62-XX) 10 Topological groups, Lie groups (22-XX) 9 Number theory (11-XX) 9 Differential geometry (53-XX) 9 Probability theory and stochastic processes (60-XX) 6 Real functions (26-XX) 6 Computer science (68-XX) 5 Nonassociative rings and algebras (17-XX) 5 Ordinary differential equations (34-XX) 4 Mechanics of particles and systems (70-XX) 4 Optics, electromagnetic theory (78-XX) 4 Biology and other natural sciences (92-XX) 3 Field theory and polynomials (12-XX) 3 Operations research, mathematical programming (90-XX) 2 Difference and functional equations (39-XX) 2 Fluid mechanics (76-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Sequences, series, summability (40-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of deformable solids (74-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Citations by Year