Abstract
We investigate an approximation of functions on subsets ℝ n in the space L p with 2 ⩽ p < ∞ by linear combinations of the indicators of balls. We consider the case where the radii of balls are proportional to positive zeros of a Bessel function.
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References
N. I. Achiezer, Theory of Approximation, Ungar, New York, 1956.
R. E. Edwards, Fourier Series: a Modern Introduction, Springer, New York, 1982.
L. H. Loomis, An Introduction to Abstrtact Harmonic Analysis, Van Nostrand, New York, 1953.
V. V. Volchkov, Integral Geometry and Convolution Equations, Kluwer, Dordrecht, 2003.
V. V. Volchkov and Vit. V. Volchkov, Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group, Springer, London, 2009.
V. V. Volchkov and Vit. V. Volchkov, Offbeat Integral Geometry on Symmetric Spaces, Birkhäuser, Basel, 2013.
E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, 1971.
O. A. Ochakovskaya, “The theorems of spherical means for solutions of the Helmholtz equation on unbounded domains,” Izv. Ross. Akad. Nauk. Ser. Mat., 76, No. 2, 161–170 (2012).
L. Hӧrmander, The Analysis of Linear Partial Differential Operators: Distribution Theory and Fourier Analysis, Springer, Berlin, 2003, Vol. 1.
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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 12, No. 4, pp. 472–483, September–December, 2015.
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Ochakovskaya, O.A. Approximation in L p by linear combinations of the indicators of balls. J Math Sci 218, 39–46 (2016). https://doi.org/10.1007/s10958-016-3009-5
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DOI: https://doi.org/10.1007/s10958-016-3009-5