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Meaney, Christopher

Divergent Jacobi polynomial series. (English) Zbl 0488.42031

Proc. Am. Math. Soc. 87, 459-462 (1983).
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Cited in 13 Documents

MSC:

42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
42C25 Uniqueness and localization for orthogonal series
43A85 Harmonic analysis on homogeneous spaces
58J99 Partial differential equations on manifolds; differential operators

Keywords:

Jacobi polynomial series; localization; spherical harmonic expansions
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References:

[1] Richard Askey, Jacobi polynomial expansions with positive coefficients and imbeddings of projective spaces, Bull. Amer. Math. Soc. 74 (1968), 301 – 304. · Zbl 0167.35003
[2] R. Askey and N. H. Bingham, Gaussian processes on compact symmetric spaces, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 37 (1976/77), no. 2, 127 – 143. · Zbl 0329.60019 · doi:10.1007/BF00536776
[3] V. M. Badkov, Approximate properties of Fourier series in orthogonal polynomials, Uspekhi Mat. Nauk 33 (1978), no. 4(202), 51 – 106, 255 (Russian).
[4] S. Chanillo, On the weak behaviour of partial sums of Legendre series, Trans. Amer. Math. Soc. 268 (1981), no. 2, 367 – 376. · Zbl 0534.42005
[5] B. Dreseler and P. M. Soardi, A Cohen-type inequality for Jacobi expansions and divergence of Fourier series on compact symmetric spaces, J. Approx. Theory 35 (1982), no. 3, 214 – 221. · Zbl 0494.42001 · doi:10.1016/0021-9045(82)90003-X
[6] SigurÄ’ur Helgason, The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds, Acta Math. 113 (1965), 153 – 180. · Zbl 0163.16602 · doi:10.1007/BF02391776
[7] Carlos E. Kenig and Peter A. Tomas, The weak behavior of spherical means, Proc. Amer. Math. Soc. 78 (1980), no. 1, 48 – 50. · Zbl 0432.42014
[8] C. Meaney, Localization and uniqueness of spherical harmonic expansions, Ph.D. dissertation, Dept. Math., Univ. of Washington, Seattle, 1979. · Zbl 0543.43006
[9] Benjamin Muckenhoupt, Mean convergence of Jacobi series, Proc. Amer. Math. Soc. 23 (1969), 306 – 310. · Zbl 0182.39701
[10] Jerome Newman and Walter Rudin, Mean convergence of orthogonal series, Proc. Amer. Math. Soc. 3 (1952), 219 – 222. · Zbl 0046.29402
[11] Harry Pollard, The convergence almost everywhere of Legendre series, Proc. Amer. Math. Soc. 35 (1972), 442 – 444. · Zbl 0266.42011
[12] Robert J. Stanton and Peter A. Tomas, Polyhedral summability of Fourier series on compact Lie groups, Amer. J. Math. 100 (1978), no. 3, 477 – 493. · Zbl 0421.43009 · doi:10.2307/2373834
[13] G. Szegö, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R. I., 1969. · JFM 65.0278.03
[14] A. Zygmund, Trigonometric series: Vols. I, II, Second edition, reprinted with corrections and some additions, Cambridge University Press, London-New York, 1968.
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