Research output per year
Research output per year
- 42 results
Search results
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2024
Needlets liberated
Brauchart, J. S., Grabner, P. J., Sloan, I. H. & Womersley, R. S., Nov 2024, In: Applied and Computational Harmonic Analysis. 73, 101693.Research output: Contribution to journal › Article › peer-review
Open Access -
2023
Complete Minimal Logarithmic Energy Asymptotics for Points in a Compact Interval: A Consequence of the Discriminant of Jacobi Polynomials
Brauchart, J., 30 Dec 2023, In: Constructive Approximation. 19 p.Research output: Contribution to journal › Article › peer-review
Open AccessFile -
2022
Weighted L2-norms of Gegenbauer polynomials
Brauchart, J. & Grabner, P., Aug 2022, In: Aequationes Mathematicae. 96, 4, p. 741-762 22 p.Research output: Contribution to journal › Article
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2020
Hyperuniform point sets on the sphere: probabilistic aspects
Brauchart, J. S., Grabner, P. J., Kusner, W. B. & Ziefle, J., 1 Aug 2020, In: Monatshefte für Mathematik. 192, 4, p. 763–781 19 p.Research output: Contribution to journal › Article › peer-review
Open Access -
2019
External Fields and Uniform Distribution in Squares and Cubes
Brauchart, J., 11 Sept 2019. 1 p.Research output: Contribution to conference › Poster
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Hyperuniform point sets on the sphere: deterministic aspects
Brauchart, J., Grabner, P. & Kusner, W., 2019, In: Constructive Approximation. 2019, 50, p. 45–61 17 p.Research output: Contribution to journal › Article › peer-review
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2018
Explicit families of functions on the sphere with exactly known Sobolev space smoothness
Brauchart, J. S., 23 May 2018, Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan. Springer International Publishing AG , p. 153-177 25 p.Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review
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Logarithmic and riesz equilibrium for multiple sources on the sphere: The exceptional case
Brauchart, J. S., Dragnev, P. D., Saff, E. B. & Womersley, R. S., 23 May 2018, Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan. Springer International Publishing AG , p. 179-203 25 p.Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review
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2016
Explicit formulas for the Riesz energy of the Nth roots of unity
Brauchart, J., 2016, Modern trends in constructive function theory: Papers from the Constructive Functions 2014 Conference in honor of Ed Saff's 70th birthday held at Vanderbilt University, Nashville, TN, May 26–30, 2014. Edited by Douglas P. Hardin, Doron S. Lubinsky and Brian Z. Simanek. American Mathematical Society, Vol. 661. p. 101-120 (Contemporary Mathematics).Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review
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Minimal Energy, External Fields, and Numerical Integration on a Sphere
Brauchart, J., 2016, 390 p.Research output: Thesis › Habilitation
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Random Point Sets on the Sphere --- Hole Radii, Covering, and Separation
Brauchart, J., Reznikov, A. B., Saff, E. B., Sloan, I. H., Wang, Y. & Womersley, R. S., 4 Oct 2016, In: Experimental Mathematics. 20 p.Research output: Contribution to journal › Article › peer-review
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2015
Covering of spheres by spherical caps and worst-case error for equal weight cubature in Sobolev spaces
Brauchart, J., Dick, J., Saff, E. B., Sloan, I. H., Wang, Y. G. & Womersley, R. S., 2015, In: Journal of Mathematical Analysis and Applications. 431, 2, p. 782-811Research output: Contribution to journal › Article › peer-review
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Distributing many points on spheres: minimal energy and designs
Brauchart, J. & Grabner, P., 2015, In: Journal of Complexity. 31, 3, p. 293-326Research output: Contribution to journal › Article › peer-review
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Spatial low-discrepancy sequences, spherical cone discrepancy, and applications in financial modeling
Brauchart, J., Dick, J. & Fang, L., 2015, In: Journal of Computational and Applied Mathematics. 286, p. 28-53Research output: Contribution to journal › Article › peer-review
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2014
An Electrostatics Problem on the Sphere Arising from a Nearby Point Charge
Brauchart, J., Dragnev, P. & Saff, E. B., 2014, Constructive Theory of Functions Sozopol 2013. Sofia: Prof. Marin Drinov Academic Publishing House, p. 11-55Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review
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Optimal N-Point Configurations on the Sphere: “Magic” Numbers and Smale’s 7th Problem
Nerattini, R., Brauchart, J. & Kiessling, M., 2014, In: Journal of Statistical Physics. 157, p. 1138-1206Research output: Contribution to journal › Article › peer-review
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QMC designs: Optimal order Quasi Monte Carlo integration schemes on the sphere
Brauchart, J., Saff, E. B., Sloan, I. H. & Womersley, R. S., 2014, In: Mathematics of Computation. 83, 290, p. 2821-2851Research output: Contribution to journal › Article › peer-review
Open Access -
Riesz External Field Problems on the Hypersphere and Optimal Point Separation
Brauchart, J., Dragnev, P. & Saff, E. B., 2014, In: Potential analysis. 41, 3, p. 647-678Research output: Contribution to journal › Article › peer-review
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2013
A characterization of Sobolev spaces on the sphere and an extension of Stolarsky's invariance principle to arbitrary smoothness
Brauchart, J. & Dick, J., 2013, In: Constructive Approximation. 38, 3, p. 397-445Research output: Contribution to journal › Article › peer-review
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A simple proof of Stolarsky's invariance principle
Brauchart, J. & Dick, J., 2013, In: Proceedings of the American Mathematical Society. 141, 6, p. 2085-2096Research output: Contribution to journal › Article › peer-review
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Stolarsky’s invariance principle and discrepancy of point sets on the sphere
Brauchart, J., Dick, J. & Fang, L., 2013, Abstracts from the workshop. ., Vol. 10. p. 2837-2917 (Oberwohlfach Report).Research output: Chapter in Book/Report/Conference proceeding › Conference paper
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2012
A fascinating polynomial sequence arising from an electrostatics problem on the sphere
Brauchart, J., Dragnev, P., Saff, E. B. & van de Woestijne, C. E., 2012, In: Acta Mathematica Hungarica. 137, 1-2, p. 10-26Research output: Contribution to journal › Article › peer-review
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Discrete energy asymptotics on a Riemannian circle
Brauchart, J., Hardin, D. P. & Saff, E. B., 2012, In: Uniform Distribution Theory. 7, 2, p. 77-108Research output: Contribution to journal › Article › peer-review
Open Access -
Point sets on the sphere S^2 with small spherical cap discrepancy
Aistleitner, C., Brauchart, J. & Dick, J., 2012, In: Discrete & Computational Geometry. 48, 4, p. 990-1024Research output: Contribution to journal › Article › peer-review
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Quasi-Monte Carlo rules for numerical integration over the unit sphere S^2
Brauchart, J. & Dick, J., 2012, In: Numerische Mathematik. 121, 3, p. 473-502Research output: Contribution to journal › Article › peer-review
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Spherical Nets, Sequences and Lattice rules -- construction of low-discrepancy sequences on spheres.
Brauchart, J., Aistleitner, C., Dick, J., Saff, E. B., Sloan, I. H. & Womersley, R. S., 2012, Abstracts from the workshop. ., Vol. 9. p. 2429-2492 (Oberwohlfach Report).Research output: Chapter in Book/Report/Conference proceeding › Conference paper
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The next-order term for optimal Riesz and logarithmic energy asymptotics on the sphere
Brauchart, J., Hardin, D. P. & Saff, E. B., 2012, Recent advances in orthogonal polynomials, special functions, and their applications. Providence, RI: American Mathematical Society, Vol. 578. p. 31-61 (Contemporary Mathematics).Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review
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2011
Optimal discrete Riesz energy and discrepancy
Brauchart, J., 2011, In: Uniform Distribution Theory. 6, 2, p. 207-220Research output: Contribution to journal › Article › peer-review
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2010
Menke points on the real line and their connection to classical orthogonal polynomials
Mathur, P., Brauchart, J. & Saff, E. B., 2010, In: Journal of Computational and Applied Mathematics. 233, 6, p. 1416-1431Research output: Contribution to journal › Article › peer-review
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The discrete minimal energy problem and sequences modulo one
Brauchart, J., 2010, Dependence in probability, analysis and number theory. A volume in memory of Walter Philipp.. Heber City, UT: Kendrick Press, p. 123-143Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review
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2009
Riesz Energy and Sets of Revolution in $\mathbb{R}^3$
Brauchart, J., Hardin, D. P. & Saff, E. B., 2009, Proceedings of the Conference on Functional Analysis and Complex Analysis. ., Vol. 481. p. 47-57 (Contemporary Mathematics (CONM)).Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review
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Riesz extremal measures on the sphere for axis-supported external fields
Brauchart, J., Dragnev, P. & Saff, E. B., 2009, In: Journal of Mathematical Analysis and Applications. 356, 2, p. 769-792Research output: Contribution to journal › Article › peer-review
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The Riesz energy of the $N$th roots of unity: an asymptotic expansion for large $N$
Brauchart, J., Hardin, D. P. & Saff, E. B., 2009, In: The Bulletin of the London Mathematical Society. 41, 4, p. 621-633Research output: Contribution to journal › Article › peer-review
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2008
Optimal logarithmic energy points on the unit sphere
Brauchart, J., 2008, In: Mathematics of Computation. 77, 263, p. 1599-1613Research output: Contribution to journal › Article › peer-review
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2007
Minimum Riesz s-energy points on compact sets in R^3
Brauchart, J., Hardin, D. P. & Saff, E. B., 2007, Abstracts from the mini-workshop. ., Vol. 4. p. 1027-1072 (Oberwohlfach Report).Research output: Chapter in Book/Report/Conference proceeding › Conference paper
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Numerical Integration over Spheres of Arbitrary Dimension
Brauchart, J. & Hesse, K., 2007, In: Constructive Approximation. 25, 1, p. 41-71Research output: Contribution to journal › Article › peer-review
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The support of the limit distribution of optimal Riesz energy points on sets of revolution in $\mathbb{R}^3$
Brauchart, J., Hardin, D. P. & Saff, E. B., 2007, In: Journal of Mathematical Physics. 48, 12, p. 122901-122901Research output: Contribution to journal › Article › peer-review
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2006
About the second term of the asymptotics for optimal Riesz energy on the sphere in the potential-theoretical case
Brauchart, J., 2006, In: Integral transforms and special functions. 17, 5, p. 321-328Research output: Contribution to journal › Article › peer-review
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2005
Points on an Unit Sphere in $\mathbb{R}^{d+1}$, Riesz Energy, Discrepancy and Numerical Integration
Brauchart, J., 2005Research output: Thesis › Doctoral Thesis
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2004
Invariance Principles for Energy Functionals on Spheres
Brauchart, J., 2004, In: Monatshefte für Mathematik. 141, 2, p. 101-117Research output: Contribution to journal › Article › peer-review
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2003
Note on a Generalized Invariance Principle and its Relevance for Cap Discrepancy and Energy
Brauchart, J., 2003, Modern Developments in Multivariate Approximation. Basel/Schweiz: Birkhäuser, Vol. 145. p. 41-55 (International Series of Numerical Mathematics).Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review
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2001
Punktverteilungen extremaler diskreter Energie auf Sphären
Brauchart, J., 2001Research output: Thesis › Diploma Thesis