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On convergence of orthogonal series of Bessel functions. (English) Zbl 0273.42013


MSC:

42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
34L99 Ordinary differential operators
41A30 Approximation by other special function classes
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References:

[1] Benedek A. and Panzone R. , On mean convergence of Fourier-Bessel series of negative order , Studies in App. Math. Vol. 4 n^\circ 3 , ( 1971 ), 281 - 292 . MR 310535 | Zbl 0218.42012 · Zbl 0218.42012
[2] Benedek A. and Panzone R. , Mean convergence of Bessel and Dini series, Notices AMS , 18 , n0 6 , ( 1971 ), p. 951 (to appear Rev. UMA, vol. 26 , ( 1972 ))- [3] Muckenhoupt B. , Mean convergence of Hermite and Laguerre series, II , TAMS , 147 , ( 1970 ), 433 - 460 . MR 256051 | Zbl 0191.07602 · Zbl 0191.07602
[3] Titchmarsh , E.C. , Eigenfunction expansions I , Oxford , ( 1962 ). · Zbl 0099.05201
[4] Watson , G.N. , A treatise on the theory of Bessel functions , Cambridge , ( 1952 ). Zbl 0174.36202 · Zbl 0174.36202
[5] Wing , G.M. , The mean convergence of orthogonal series , Amer. J. of Math. , LXXII , ( 1950 ), 792 - 808 . MR 37923 | Zbl 0041.38515 · Zbl 0041.38515
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