Edit Profile (opens in new tab) Brauchart, Johann S. Compute Distance To: Compute Author ID: brauchart.johann-s Published as: Brauchart, Johann S.; Brauchart, J. S. Documents Indexed: 32 Publications since 2003 Reviewing Activity: 10 Reviews Co-Authors: 17 Co-Authors with 24 Joint Publications 451 Co-Co-Authors all top 5 Co-Authors 8 single-authored 14 Saff, Edward Barry 6 Dick, Josef 5 Dragnev, Peter D. 5 Hardin, Douglas P. 4 Womersley, Robert S. 3 Grabner, Peter J. 3 Sloan, Ian Hugh 2 Kusner, Wöden 2 Wang, Yuguang 1 Aistleitner, Christoph 1 Fang, Lou 1 Hesse, Kerstin 1 Kiessling, Michael Karl-Heinz 1 Nerattini, Rachele 1 Reznikov, A. B. 1 van de Woestijne, Christiaan E. 1 Ziefle, Jonas all top 5 Serials 3 Constructive Approximation 2 Journal of Mathematical Analysis and Applications 2 Mathematics of Computation 2 Journal of Computational and Applied Mathematics 2 Monatshefte für Mathematik 2 Uniform Distribution Theory 1 Journal of Mathematical Physics 1 Journal of Statistical Physics 1 Bulletin of the London Mathematical Society 1 Numerische Mathematik 1 Proceedings of the American Mathematical Society 1 Acta Mathematica Hungarica 1 Journal of Complexity 1 Discrete & Computational Geometry 1 Experimental Mathematics 1 Potential Analysis 1 Integral Transforms and Special Functions all top 5 Fields 14 Potential theory (31-XX) 12 Approximations and expansions (41-XX) 11 Numerical analysis (65-XX) 9 Number theory (11-XX) 4 Functions of a complex variable (30-XX) 4 Special functions (33-XX) 2 Measure and integration (28-XX) 2 Functional analysis (46-XX) 2 Convex and discrete geometry (52-XX) 2 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 28 Publications have been cited 341 times in 190 Documents Cited by ▼ Year ▼ The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere. Zbl 1318.31011Brauchart, J. S.; Hardin, D. P.; Saff, E. B. 39 2012 QMC designs: optimal order quasi Monte Carlo integration schemes on the sphere. Zbl 1315.65003Brauchart, J. S.; Saff, E. B.; Sloan, I. H.; Womersley, R. S. 38 2014 Distributing many points on spheres: minimal energy and designs. Zbl 1320.65007Brauchart, Johann S.; Grabner, Peter J. 31 2015 Numerical integration over spheres of arbitrary dimension. Zbl 1106.41028Brauchart, Johann S.; Hesse, Kerstin 24 2007 Optimal logarithmic energy points on the unit sphere. Zbl 1196.41009Brauchart, J. S. 21 2008 Point sets on the sphere \(\mathbb{S}^{2}\) with small spherical cap discrepancy. Zbl 1272.65003Aistleitner, C.; Brauchart, J. S.; Dick, J. 19 2012 A simple proof of Stolarsky’s invariance principle. Zbl 1275.41024Brauchart, Johann S.; Dick, Josef 18 2013 The Riesz energy of the \(N\)th roots of unity: an asymptotic expansion for large \(N\). Zbl 1175.30003Brauchart, J. S.; Hardin, D. P.; Saff, E. B. 17 2009 Riesz extremal measures on the sphere for axis-supported external fields. Zbl 1175.31004Brauchart, J. S.; Dragnev, P. D.; Saff, E. B. 15 2009 Discrete energy asymptotics on a Riemannian circle. Zbl 1324.31006Brauchart, Johann S.; Hardin, Douglas P.; Saff, Edward B. 12 2012 Riesz external field problems on the hypersphere and optimal point separation. Zbl 1307.31010Brauchart, Johann S.; Dragnev, Peter D.; Saff, Edward B. 12 2014 About the second term of the asymptotics for optimal Riesz energy on the sphere in the potential-theoretical case. Zbl 1100.41018Brauchart, Johann S. 12 2006 A characterization of Sobolev spaces on the sphere and an extension of Stolarsky’s invariance principle to arbitrary smoothness. Zbl 1284.41013Brauchart, Johann S.; Dick, Josef 10 2013 Optimal \(N\)-point configurations on the sphere: “magic” numbers and Smale’s 7th problem. Zbl 1397.90315Nerattini, R.; Brauchart, J. S.; Kiessling, M. K.-H. 9 2014 Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces. Zbl 1325.65037Brauchart, J. S.; Dick, J.; Saff, E. B.; Sloan, I. H.; Wang, Y. G.; Womersley, R. S. 8 2015 Random point sets on the sphere – hole radii, covering, and separation. Zbl 1386.52019Brauchart, J. S.; Reznikov, A. B.; Saff, E. B.; Sloan, I. H.; Wang, Y. G.; Womersley, R. S. 8 2018 A fascinating polynomial sequence arising from an electrostatics problem on the sphere. Zbl 1299.30007Brauchart, J. S.; Dragnev, P. D.; Saff, E. B.; van de Woestijne, C. E. 6 2012 Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling. Zbl 1317.65005Brauchart, Johann S.; Dick, Josef; Fang, Lou 6 2015 Quasi-Monte Carlo rules for numerical integration over the unit sphere \({\mathbb{S}^2}\). Zbl 1258.65003Brauchart, Johann S.; Dick, Josef 6 2012 Invariance principles for energy functionals on spheres. Zbl 1052.41007Brauchart, Johann S. 5 2004 Optimal discrete Riesz energy and discrepancy. Zbl 1313.11092Brauchart, Johann S. 5 2011 Hyperuniform point sets on the sphere: deterministic aspects. Zbl 1437.11111Brauchart, Johann S.; Grabner, Peter J.; Kusner, Wöden 5 2019 The support of the limit distribution of optimal Riesz energy points on sets of revolution in \(\mathbb R^3\). Zbl 1153.81328Brauchart, J. S.; Hardin, D. P.; Saff, E. B. 4 2007 Hyperuniform point sets on the sphere: probabilistic aspects. Zbl 1457.60067Brauchart, Johann S.; Grabner, Peter J.; Kusner, Wöden; Ziefle, Jonas 4 2020 Riesz energy and sets of revolution in \(\mathbb R^3\). Zbl 1185.28008Brauchart, Johann S.; Hardin, Douglas P.; Saff, Edward B. 3 2009 Note on a generalized invariance principle and its relevance for cap discrepancy and energy. Zbl 1038.11046Brauchart, Johann S. 2 2003 Logarithmic and Riesz equilibrium for multiple sources on the sphere: the exceptional case. Zbl 1405.31007Brauchart, Johann S.; Dragnev, Peter D.; Saff, Edward B.; Womersley, Robert S. 1 2018 An electrostatics problem on the sphere arising from a nearby point charge. Zbl 1422.31004Brauchart, Johann S.; Dragnev, Peter D.; Saff, Edward B. 1 2014 Hyperuniform point sets on the sphere: probabilistic aspects. Zbl 1457.60067Brauchart, Johann S.; Grabner, Peter J.; Kusner, Wöden; Ziefle, Jonas 4 2020 Hyperuniform point sets on the sphere: deterministic aspects. Zbl 1437.11111Brauchart, Johann S.; Grabner, Peter J.; Kusner, Wöden 5 2019 Random point sets on the sphere – hole radii, covering, and separation. Zbl 1386.52019Brauchart, J. S.; Reznikov, A. B.; Saff, E. B.; Sloan, I. H.; Wang, Y. G.; Womersley, R. S. 8 2018 Logarithmic and Riesz equilibrium for multiple sources on the sphere: the exceptional case. Zbl 1405.31007Brauchart, Johann S.; Dragnev, Peter D.; Saff, Edward B.; Womersley, Robert S. 1 2018 Distributing many points on spheres: minimal energy and designs. Zbl 1320.65007Brauchart, Johann S.; Grabner, Peter J. 31 2015 Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces. Zbl 1325.65037Brauchart, J. S.; Dick, J.; Saff, E. B.; Sloan, I. H.; Wang, Y. G.; Womersley, R. S. 8 2015 Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling. Zbl 1317.65005Brauchart, Johann S.; Dick, Josef; Fang, Lou 6 2015 QMC designs: optimal order quasi Monte Carlo integration schemes on the sphere. Zbl 1315.65003Brauchart, J. S.; Saff, E. B.; Sloan, I. H.; Womersley, R. S. 38 2014 Riesz external field problems on the hypersphere and optimal point separation. Zbl 1307.31010Brauchart, Johann S.; Dragnev, Peter D.; Saff, Edward B. 12 2014 Optimal \(N\)-point configurations on the sphere: “magic” numbers and Smale’s 7th problem. Zbl 1397.90315Nerattini, R.; Brauchart, J. S.; Kiessling, M. K.-H. 9 2014 An electrostatics problem on the sphere arising from a nearby point charge. Zbl 1422.31004Brauchart, Johann S.; Dragnev, Peter D.; Saff, Edward B. 1 2014 A simple proof of Stolarsky’s invariance principle. Zbl 1275.41024Brauchart, Johann S.; Dick, Josef 18 2013 A characterization of Sobolev spaces on the sphere and an extension of Stolarsky’s invariance principle to arbitrary smoothness. Zbl 1284.41013Brauchart, Johann S.; Dick, Josef 10 2013 The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere. Zbl 1318.31011Brauchart, J. S.; Hardin, D. P.; Saff, E. B. 39 2012 Point sets on the sphere \(\mathbb{S}^{2}\) with small spherical cap discrepancy. Zbl 1272.65003Aistleitner, C.; Brauchart, J. S.; Dick, J. 19 2012 Discrete energy asymptotics on a Riemannian circle. Zbl 1324.31006Brauchart, Johann S.; Hardin, Douglas P.; Saff, Edward B. 12 2012 A fascinating polynomial sequence arising from an electrostatics problem on the sphere. Zbl 1299.30007Brauchart, J. S.; Dragnev, P. D.; Saff, E. B.; van de Woestijne, C. E. 6 2012 Quasi-Monte Carlo rules for numerical integration over the unit sphere \({\mathbb{S}^2}\). Zbl 1258.65003Brauchart, Johann S.; Dick, Josef 6 2012 Optimal discrete Riesz energy and discrepancy. Zbl 1313.11092Brauchart, Johann S. 5 2011 The Riesz energy of the \(N\)th roots of unity: an asymptotic expansion for large \(N\). Zbl 1175.30003Brauchart, J. S.; Hardin, D. P.; Saff, E. B. 17 2009 Riesz extremal measures on the sphere for axis-supported external fields. Zbl 1175.31004Brauchart, J. S.; Dragnev, P. D.; Saff, E. B. 15 2009 Riesz energy and sets of revolution in \(\mathbb R^3\). Zbl 1185.28008Brauchart, Johann S.; Hardin, Douglas P.; Saff, Edward B. 3 2009 Optimal logarithmic energy points on the unit sphere. Zbl 1196.41009Brauchart, J. S. 21 2008 Numerical integration over spheres of arbitrary dimension. Zbl 1106.41028Brauchart, Johann S.; Hesse, Kerstin 24 2007 The support of the limit distribution of optimal Riesz energy points on sets of revolution in \(\mathbb R^3\). Zbl 1153.81328Brauchart, J. S.; Hardin, D. P.; Saff, E. B. 4 2007 About the second term of the asymptotics for optimal Riesz energy on the sphere in the potential-theoretical case. Zbl 1100.41018Brauchart, Johann S. 12 2006 Invariance principles for energy functionals on spheres. Zbl 1052.41007Brauchart, Johann S. 5 2004 Note on a generalized invariance principle and its relevance for cap discrepancy and energy. Zbl 1038.11046Brauchart, Johann S. 2 2003 all cited Publications top 5 cited Publications all top 5 Cited by 229 Authors 21 Saff, Edward Barry 18 Brauchart, Johann S. 11 Hardin, Douglas P. 8 Beltrán, Carlos 7 Dick, Josef 7 Dragnev, Peter D. 7 Etayo, Ujué 7 Wang, Yuguang 7 Womersley, Robert S. 6 Henrion, René 6 Sloan, Ian Hugh 5 Grabner, Peter J. 5 Marzo, Jordi 5 Petrache, Mircea 5 Serfaty, Sylvia 5 Skriganov, Maxim M. 5 Steinerberger, Stefan 4 Bétermin, Laurent 4 Dai, Feng 4 Dubinin, Vladimir N. 4 Heitsch, Holger 4 Hesse, Kerstin 4 López García, Abey 4 Ortega-Cerdà, Joaquim 4 Pausinger, Florian 4 Stepanyuk, Tetiana A. 3 Basu, Kinjal 3 Bilogliadov, Mykhailo 3 Bilyk, Dmitry 3 Ehler, Martin 3 Gräf, Manuel 3 Harbrecht, Helmut 3 Hirao, Masatake 3 Kiessling, Michael Karl-Heinz 3 Leopardi, Paul Charles 3 Mhaskar, Hrushikesh N. 3 Owen, Art B. 3 Van Ackooij, Wim 3 Vlasiuk, Oleksandr V. 3 Wendland, Wolfgang L. 3 Wielonsky, Franck 3 Zorii, Natalia 2 Baake, Michael 2 Benko, David 2 Bloom, Thomas 2 Breger, Anna 2 Coons, Michael 2 Edelsbrunner, Herbert 2 Erdélyi, Tamás 2 Kusner, Wöden 2 Le Gia, Quoc Thong 2 Leblé, Thomas 2 Levenberg, Norman jun. 2 Lin, Shaobo 2 Malyshev, Vadim Aleksandrovich 2 Matzke, Ryan W. 2 McCleary, Ryan E. 2 Michel, Volker 2 Oates, Chris J. 2 Orive Rodríguez, Ramón Angel 2 Osting, Braxton 2 Pérez-Aros, Pedro 2 Pillichshammer, Friedrich 2 Prilepkina, Elena Gumarovna 2 Sandier, Etienne 2 Schultz, Rüdiger 2 Sidi, Avram 2 Simanek, Brian Z. 2 Sonnleitner, Mathias 2 Sun, Xingping 2 Thäle, Christoph 2 Wang, Heping 2 Zhu, Houying 1 Adelhütte, Dennis 1 Afanaseva-Grigoreva, Anna Sergeevna 1 Aistleitner, Christoph 1 Alberti, Giovanni S. 1 Ambrus, Gergely 1 Aßmann, Denis 1 Barg, Alexander M. 1 Bell, Paul C. 1 Bellet, Jean-Baptiste 1 Berman, Robert J. 1 Besau, Florian 1 Borodachov, Sergiy V. 1 Brachet, Matthieu 1 Brandolini, Luca 1 Breda, Ana Maria D’Azevedo 1 Brown, Louis 1 Burjons, Elisabet 1 Calef, Matthew T. 1 Cao, Feilong 1 Carfagna, Melania 1 Chen, Chun 1 Chen, William Wai Lim 1 Chen, Xiaojun 1 Chen, Xuemei 1 Chen, Zhenzhong 1 Christensen, Ole 1 Coeurjolly, David ...and 129 more Authors all top 5 Cited in 85 Serials 17 Constructive Approximation 14 Journal of Complexity 10 Journal of Mathematical Analysis and Applications 9 Journal of Approximation Theory 7 Mathematics of Computation 5 Journal of Mathematical Physics 5 Proceedings of the American Mathematical Society 5 Transactions of the American Mathematical Society 5 Discrete & Computational Geometry 4 Journal of Computational and Applied Mathematics 4 Mathematika 4 Advances in Computational Mathematics 3 Computers & Mathematics with Applications 3 SIAM Journal on Numerical Analysis 3 Potential Analysis 2 Archive for Rational Mechanics and Analysis 2 Bulletin of the Australian Mathematical Society 2 Journal of Statistical Physics 2 Monatshefte für Mathematik 2 Numerische Mathematik 2 Indagationes Mathematicae. New Series 2 Applied and Computational Harmonic Analysis 2 Electronic Journal of Probability 2 The Journal of Fourier Analysis and Applications 2 Foundations of Computational Mathematics 2 Computational Methods and Function Theory 2 GEM - International Journal on Geomathematics 2 Analysis and Mathematical Physics 2 Statistics and Computing 1 Problems of Information Transmission 1 Advances in Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 The Annals of Statistics 1 Applied Mathematics and Computation 1 Inventiones Mathematicae 1 Journal of Functional Analysis 1 Journal of Number Theory 1 Journal of Statistical Planning and Inference 1 Mathematische Nachrichten 1 Michigan Mathematical Journal 1 Pacific Journal of Mathematics 1 Siberian Mathematical Journal 1 Statistics & Probability Letters 1 Chinese Annals of Mathematics. Series B 1 Acta Mathematica Hungarica 1 Acta Applicandae Mathematicae 1 ACM Transactions on Graphics 1 Probability Theory and Related Fields 1 Algorithmica 1 Numerical Methods for Partial Differential Equations 1 Journal of the American Mathematical Society 1 IMRN. International Mathematics Research Notices 1 The Journal of Geometric Analysis 1 Numerical Algorithms 1 SIAM Journal on Mathematical Analysis 1 Mathematical Programming. Series A. Series B 1 Journal of Dynamics and Differential Equations 1 SIAM Journal on Optimization 1 Journal of Mathematical Imaging and Vision 1 Experimental Mathematics 1 Journal of Convex Analysis 1 Engineering Analysis with Boundary Elements 1 Doklady Mathematics 1 Computing and Visualization in Science 1 Vietnam Journal of Mathematics 1 Mathematical Methods of Operations Research 1 Journal of Combinatorial Optimization 1 Journal for Geometry and Graphics 1 Mathematical Inequalities & Applications 1 Journal of Machine Learning Research (JMLR) 1 SIAM Journal on Applied Dynamical Systems 1 Journal of the Institute of Mathematics of Jussieu 1 International Journal of Wavelets, Multiresolution and Information Processing 1 Computational Management Science 1 Sibirskie Èlektronnye Matematicheskie Izvestiya 1 Electronic Journal of Statistics 1 Mathematical Geosciences 1 Algorithms 1 Advances in Mathematical Physics 1 JSIAM Letters 1 Problemy Analiza. Issues of Analysis 1 SIAM/ASA Journal on Uncertainty Quantification 1 Research in the Mathematical Sciences 1 Advances in Data Science and Adaptive Analysis 1 Japanese Journal of Statistics and Data Science all top 5 Cited in 43 Fields 58 Numerical analysis (65-XX) 52 Potential theory (31-XX) 40 Approximations and expansions (41-XX) 39 Number theory (11-XX) 22 Probability theory and stochastic processes (60-XX) 20 Convex and discrete geometry (52-XX) 17 Statistical mechanics, structure of matter (82-XX) 16 Harmonic analysis on Euclidean spaces (42-XX) 15 Operations research, mathematical programming (90-XX) 13 Special functions (33-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 9 Partial differential equations (35-XX) 8 Measure and integration (28-XX) 8 Functions of a complex variable (30-XX) 8 Statistics (62-XX) 6 Functional analysis (46-XX) 6 Mechanics of deformable solids (74-XX) 5 Combinatorics (05-XX) 5 Computer science (68-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Information and communication theory, circuits (94-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Operator theory (47-XX) 3 Differential geometry (53-XX) 3 Mechanics of particles and systems (70-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Algebraic geometry (14-XX) 2 Real functions (26-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Fluid mechanics (76-XX) 2 Optics, electromagnetic theory (78-XX) 2 Quantum theory (81-XX) 2 Geophysics (86-XX) 2 Systems theory; control (93-XX) 1 History and biography (01-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 General topology (54-XX) 1 Manifolds and cell complexes (57-XX) 1 Biology and other natural sciences (92-XX) Citations by Year