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Numerical integration and function approximation on compact Riemannian manifolds based on eigenfunctions of the Laplace-Beltrami operator have been widely studied in the recent literature.
D. L. Ragozin, Polynomial approximation on compact manifolds and homogeneous spaces , Trans. Amer. Math. Soc. 150
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E. M. Stein, Singular integrals and differentiability properties of functions , Princeton University Press, 1970
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A. T. James and A. G. Constantine, Generalized Jacobi polynomials as spherical functions of the Grassmann manifold , Proc. London Math. Soc. 29
1974
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P. Seymour and T. Zaslavsky, Averaging sets: a generalization of mean values and spherical designs , Advances in Math. 52
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L. Hörmander, The analysis of linear partial differential operators, I, II, III, IV , Springer Verlag, 1983-1985
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A. W. Davis, Spherical functions on the Grassmann manifold and generalized Jacobi polynomials – part 1 , Lin. Alg. Appl. 289
1999
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C. Bachoc, R. Coulangeon, and G. Nebe, Designs in Grassmannian spaces and lattices , J. Algebraic Combinatorics 16
2002
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Y. Chikuse, Statistics on special manifolds , Lecture Notes in Statistics, Springer, New York, 2003
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C. Bachoc, E. Bannai, and R. Coulangeon, Codes and designs in Grassmannian spaces , Discrete Mathematics 277
2004
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P. de la Harpe and C. Pache, Cubature formulas, geometrical designs, reproducing kernels, and Markov operators , Infinite groups: geometric, combinatorial and dynamical aspects (Basel), vol. 248, Birkhäuser, 2005, pp. 219–267
2005
Cited alongside, same era.
C. Bachoc, Linear programming bounds for codes in Grassmannian spaces , IEEE Trans. Inf. Th. 52
2006
Cited alongside, same era.
Q. T. Le Gia and H. N. Mhaskar, Polynomial operators and local approximation of solutions of pseudo-differential operators on the sphere , Numerische Mathematik 103
2006
Cited alongside, same era.
I. Dumitriu, A. Edelman, and G. Shuman, MOPS: Multivariate orthogonal polynomials (symbolically) , Journal of Symbolic Computation 42
2007
E. Novak and H. Wozniakowski, Tractability of Multivariate Problems. Volume II , EMS Tracts in Mathematics, vol. 12, EMS Publishing House, Zürich, 2010
2010
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D. Geller and I. Z. Pesenson, Band-limited localized Parseval frames and Besov spaces on compact homogeneous manifolds , J. Geom. Anal. 21
2011
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M. Ehler, F. Filbir, and H. N. Mhaskar, Locally learning biomedical data using diffusion frames , J. Comput. Biol. 19
2012
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I. Z. Pesenson and D. Geller, Cubature formulas and discrete fourier transform on compact manifolds , From Fourier Analysis and Number Theory to Radon Transforms and Geometry, vol. 28, 2012, pp. 431–453
2012
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A. Bondarenko, D. Radchenko, and M. Viazovska, Optimal asymptotic bounds for spherical designs , Ann. Math. 178
2013
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Cited alongside, same era.
P.-A. Absil, R. Mahony, and R. Sepulchre, Optimization algorithms on matrix manifolds , Princeton University Press, 2008
2008
Cited alongside, same era.
M. Maggioni and H. N. Mhaskar, Diffusion polynomial frames on metric measure spaces , Appl. Comput. Harmon. Anal. 24
2008
Cited alongside, same era.
F. Filbir and H. N. Mhaskar, A quadrature formula for diffusion polynomials corresponding to a generalized heat kernel , J. Fourier Anal. Appl. 16
2010
Cited alongside, same era.
H. N. Mhaskar, Eignets for function approximation on manifolds , Appl. Comput. Harmon. Anal. 29
2010
Cited alongside, same era.
Later among the works it cites.
M. Gräf, Efficient algorithms for the computation of optimal quadrature points on Riemannian manifolds , Universitätsverlag Chemnitz, 2013
2013
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L. Brandolini, C. Choirat, L. Colzani, G. Gigante, R. Seri, and G. Travaglini, Quadrature rules and distribution of points on manifolds , Annali della Scuola Normale Superiore di Pisa - Classe di Scienze XIII
2014
Later among the works it cites.
J. Brauchart, E. Saff, I. H. Sloan, and R. Womersley, QMC designs: Optimal order quasi Monte Carlo integration schemes on the sphere , Math. Comp. 83
2014
Later among the works it cites.
M. Ehler and M. Gräf, Harmonic decompositions on unions of Grassmannians , arXiv (2016)
2016
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