Boundedness of difference kernels of Bessel and Fourier series

Author:
Shih-hsiung Tung

Journal:
Math. Comp. **20** (1966), 157-163

MSC:
Primary 33.25

DOI:
https://doi.org/10.1090/S0025-5718-1966-0193289-6

MathSciNet review:
0193289

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**[1]**E. W. Hobson, "On the representation of a function by series of Bessel functions,"*Proc. London Math. Soc.*, (2), v. 7, 1909, pp. 359-388.**[2]**E. W. Hobson,*The Theory of Functions of a Real Variable and the Theory of Fourier Series*, Vol. II, Dover, New York, 1958. MR**19**, 1166.**[3]**K. Knopp,*Theory and Application of Infinite Series*, Blackie, London, 1957.**[4]**I. P. Natanson,*Teoriya funkciĭ veščestvennoĭ peremennoĭ*, Gosudarstv. Izdat. Tehn.-Teor. Lit.,], Moscow-Leningrad, 1950 (Russian). MR**0039790****[5]**E. C. Titchmarsh,*The Theory of Functions*, Oxford Univ. Press, London, 1939.**[6]**E. C. Titchmarsh,*Eigenfunction Expansions Associated with Second-Order Differential Equations*, Oxford, at the Clarendon Press, 1946 (German). MR**0019765****[7]**G. N. Watson,*A Treatise on the Theory of Bessel Functions*, Cambridge University Press, Cambridge, England; The Macmillan Company, New York, 1944. MR**0010746****[8]**W. H. Young, "On series of Bessel functions,"*Proc. London Math. Soc.*, (2), v. 18, 1920, pp. 163-200.

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DOI:
https://doi.org/10.1090/S0025-5718-1966-0193289-6

Article copyright:
© Copyright 1966
American Mathematical Society