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Brauchart, Johann S.

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Author ID: brauchart.johann-s Recent zbMATH articles by "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

Publications by Year

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 1318.31011
Brauchart, J. S.; Hardin, D. P.; Saff, E. B.
39
2012
QMC designs: optimal order quasi Monte Carlo integration schemes on the sphere. Zbl 1315.65003
Brauchart, J. S.; Saff, E. B.; Sloan, I. H.; Womersley, R. S.
38
2014
Distributing many points on spheres: minimal energy and designs. Zbl 1320.65007
Brauchart, Johann S.; Grabner, Peter J.
31
2015
Numerical integration over spheres of arbitrary dimension. Zbl 1106.41028
Brauchart, Johann S.; Hesse, Kerstin
24
2007
Optimal logarithmic energy points on the unit sphere. Zbl 1196.41009
Brauchart, J. S.
21
2008
Point sets on the sphere \(\mathbb{S}^{2}\) with small spherical cap discrepancy. Zbl 1272.65003
Aistleitner, C.; Brauchart, J. S.; Dick, J.
19
2012
A simple proof of Stolarsky’s invariance principle. Zbl 1275.41024
Brauchart, Johann S.; Dick, Josef
18
2013
The Riesz energy of the \(N\)th roots of unity: an asymptotic expansion for large \(N\). Zbl 1175.30003
Brauchart, J. S.; Hardin, D. P.; Saff, E. B.
17
2009
Riesz extremal measures on the sphere for axis-supported external fields. Zbl 1175.31004
Brauchart, J. S.; Dragnev, P. D.; Saff, E. B.
15
2009
Discrete energy asymptotics on a Riemannian circle. Zbl 1324.31006
Brauchart, Johann S.; Hardin, Douglas P.; Saff, Edward B.
12
2012
Riesz external field problems on the hypersphere and optimal point separation. Zbl 1307.31010
Brauchart, 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 1100.41018
Brauchart, Johann S.
12
2006
A characterization of Sobolev spaces on the sphere and an extension of Stolarsky’s invariance principle to arbitrary smoothness. Zbl 1284.41013
Brauchart, Johann S.; Dick, Josef
10
2013
Optimal \(N\)-point configurations on the sphere: “magic” numbers and Smale’s 7th problem. Zbl 1397.90315
Nerattini, 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 1325.65037
Brauchart, 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 1386.52019
Brauchart, 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 1299.30007
Brauchart, 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 1317.65005
Brauchart, Johann S.; Dick, Josef; Fang, Lou
6
2015
Quasi-Monte Carlo rules for numerical integration over the unit sphere \({\mathbb{S}^2}\). Zbl 1258.65003
Brauchart, Johann S.; Dick, Josef
6
2012
Invariance principles for energy functionals on spheres. Zbl 1052.41007
Brauchart, Johann S.
5
2004
Optimal discrete Riesz energy and discrepancy. Zbl 1313.11092
Brauchart, Johann S.
5
2011
Hyperuniform point sets on the sphere: deterministic aspects. Zbl 1437.11111
Brauchart, 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 1153.81328
Brauchart, J. S.; Hardin, D. P.; Saff, E. B.
4
2007
Hyperuniform point sets on the sphere: probabilistic aspects. Zbl 1457.60067
Brauchart, Johann S.; Grabner, Peter J.; Kusner, Wöden; Ziefle, Jonas
4
2020
Riesz energy and sets of revolution in \(\mathbb R^3\). Zbl 1185.28008
Brauchart, 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 1038.11046
Brauchart, Johann S.
2
2003
Logarithmic and Riesz equilibrium for multiple sources on the sphere: the exceptional case. Zbl 1405.31007
Brauchart, 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 1422.31004
Brauchart, Johann S.; Dragnev, Peter D.; Saff, Edward B.
1
2014
Hyperuniform point sets on the sphere: probabilistic aspects. Zbl 1457.60067
Brauchart, Johann S.; Grabner, Peter J.; Kusner, Wöden; Ziefle, Jonas
4
2020
Hyperuniform point sets on the sphere: deterministic aspects. Zbl 1437.11111
Brauchart, Johann S.; Grabner, Peter J.; Kusner, Wöden
5
2019
Random point sets on the sphere – hole radii, covering, and separation. Zbl 1386.52019
Brauchart, 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 1405.31007
Brauchart, Johann S.; Dragnev, Peter D.; Saff, Edward B.; Womersley, Robert S.
1
2018
Distributing many points on spheres: minimal energy and designs. Zbl 1320.65007
Brauchart, 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 1325.65037
Brauchart, 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 1317.65005
Brauchart, Johann S.; Dick, Josef; Fang, Lou
6
2015
QMC designs: optimal order quasi Monte Carlo integration schemes on the sphere. Zbl 1315.65003
Brauchart, 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 1307.31010
Brauchart, 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 1397.90315
Nerattini, R.; Brauchart, J. S.; Kiessling, M. K.-H.
9
2014
An electrostatics problem on the sphere arising from a nearby point charge. Zbl 1422.31004
Brauchart, Johann S.; Dragnev, Peter D.; Saff, Edward B.
1
2014
A simple proof of Stolarsky’s invariance principle. Zbl 1275.41024
Brauchart, 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 1284.41013
Brauchart, Johann S.; Dick, Josef
10
2013
The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere. Zbl 1318.31011
Brauchart, J. S.; Hardin, D. P.; Saff, E. B.
39
2012
Point sets on the sphere \(\mathbb{S}^{2}\) with small spherical cap discrepancy. Zbl 1272.65003
Aistleitner, C.; Brauchart, J. S.; Dick, J.
19
2012
Discrete energy asymptotics on a Riemannian circle. Zbl 1324.31006
Brauchart, Johann S.; Hardin, Douglas P.; Saff, Edward B.
12
2012
A fascinating polynomial sequence arising from an electrostatics problem on the sphere. Zbl 1299.30007
Brauchart, 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 1258.65003
Brauchart, Johann S.; Dick, Josef
6
2012
Optimal discrete Riesz energy and discrepancy. Zbl 1313.11092
Brauchart, Johann S.
5
2011
The Riesz energy of the \(N\)th roots of unity: an asymptotic expansion for large \(N\). Zbl 1175.30003
Brauchart, J. S.; Hardin, D. P.; Saff, E. B.
17
2009
Riesz extremal measures on the sphere for axis-supported external fields. Zbl 1175.31004
Brauchart, J. S.; Dragnev, P. D.; Saff, E. B.
15
2009
Riesz energy and sets of revolution in \(\mathbb R^3\). Zbl 1185.28008
Brauchart, Johann S.; Hardin, Douglas P.; Saff, Edward B.
3
2009
Optimal logarithmic energy points on the unit sphere. Zbl 1196.41009
Brauchart, J. S.
21
2008
Numerical integration over spheres of arbitrary dimension. Zbl 1106.41028
Brauchart, 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 1153.81328
Brauchart, 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 1100.41018
Brauchart, Johann S.
12
2006
Invariance principles for energy functionals on spheres. Zbl 1052.41007
Brauchart, Johann S.
5
2004
Note on a generalized invariance principle and its relevance for cap discrepancy and energy. Zbl 1038.11046
Brauchart, Johann S.
2
2003
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