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On mean convergence of Fourier-Bessel series of negative order. (English) Zbl 0218.42012


MSC:

42A15 Trigonometric interpolation
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization
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References:

[1] Hochstadt, The mean convergence of Fourier-Bessel Series, Siam Review 9 (2) pp 211– (1967) · Zbl 0192.42904
[2] Kaczmarz, Theorie der Orthogonalreihen (1951)
[3] Macrobert, Asymptotic expressions for the Bessel functions and the Fourier-Bessel expansions, Proc. of the Edinburgh Math. Soc. XXXIX pp 13– (1921)
[4] Okikiolu, On certain extensions of the Hilbert operator, Math. Ann. 169 pp 315– (1967) · Zbl 0149.08402
[5] Watson, A treatise on the theory of Bessel functions (1952)
[6] Whittaker, A course of modern analysis (1952)
[7] Wing, The mean convergence of orthogonal series, American J. of Math. LXXII pp 792– (1950) · Zbl 0045.33801
[8] Young, On series of Bessel functions, Proc. of the London Math. Soc. 18 pp 163– (1919) · JFM 47.0343.01
[9] Hardy, Inequalities (1952)
[10] Hardy, Some more theorems concerning Fourier series and Fourier power series, Duke Math. J. II pp 354– (1963)
[11] Muckenhoupt, Mean convergence of Jacobi series, Proc. A.M.S. 23 pp 306– (1969) · Zbl 0182.39701
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