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References
Gronwall, T.H.: On the degree of convergence of Laplace series. Trans. Amer. Math. Soc.15, 1–30 (1914).
Müller, C.: Spherical harmonics. Lecture notes in Mathematics, no. 17, Berlin: Springer 1966.
Peetre, J.: Absolute convergence of eigenfunction expansions. Math. Ann.169, 307–314 (1967).
Ragozin, D.L.: Polynomial approximation on compact manifolds and homogeneous spaces. Trans. Amer. Math. Soc.150, 41–53 (1970).
-- Constructive polynomial approximation on spheres and projective spaces. Trans. Amer. Math. Soc.162, (1971).
-- Absolute convergence of spherical harmonic expansions. (In preparation.)
Rau, H.: Über die Lebesgueschen Konstanten der Reihenentwicklungen nach Jacobischen Polynomen. J. Reine Angew. Math.161, 237–254 (1933).
Szegö, G.: Orthogonal polynomials. American Mathematical Society Colloquium Publications, Vol. XXIII. American Mathematical Society, Providence, R.I. 1959. MR 21 no. 5029.
Tai, S.S.: Minimum embeddings of compact symmetryc spaces of rank one. J. Differential Geometry2, 55–66 (1968), MR 37 no. 6950.
Taylor, M.E.: Fourier series on compact Lie group. Proc. Amer. Math. Soc.19, 1103–1105 (1968). MR 37 no. 6690.
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A version of this paper was presented to the American Mathematical Society June 15, 1968. Results related to this paper are in the author's Ph. D. thesis.
Research partially supported by NSF grant GP-9003.
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Ragozin, D.L. Uniform convergence of spherical harmonic expansions. Math. Ann. 195, 87–94 (1971). https://doi.org/10.1007/BF01419614
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DOI: https://doi.org/10.1007/BF01419614