On Absolute Convergence of Fourier Integrals
E. Liflyand
Source: Real Anal. Exchange Volume 36, Number 2
(2010), 353-360.
Abstract
New sufficient conditions for representation of a function as an absolutely convergent Fourier integral are obtained in the paper.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.rae/1321020505
Zentralblatt MATH identifier: 06032456
Mathematical Reviews number (MathSciNet): MR3016721
References
O. V. Besov, Hörmander's theorem on Fourier multipliers, Trudy Mat. Inst. Steklov 173 (1986), 164–180 (Russian). - English transl.: Proc. Steklov Inst. Math. 4 (1987), 4–14.
Mathematical Reviews (MathSciNet): MR864830
I. I. Hirschman, Jr., On multiplier transformations, I, Duke Math. J. 26 (1959), 221–242; II, ibid 28 (1961), 45–56.
Mathematical Reviews (MathSciNet): MR104973
Zentralblatt MATH: 0085.09201
Digital Object Identifier: doi:10.1215/S0012-7094-59-02623-7
Project Euclid: euclid.dmj/1077468477
J.-P. Kahane, Séries de Fourier absolument convergentes, Springer, Berlin, 1970.
Mathematical Reviews (MathSciNet): MR275043
A. Kufner, L. E. Persson, Weighted Inequalities of Hardy Type, World Scientific, 2003.
Mathematical Reviews (MathSciNet): MR1982932
Zentralblatt MATH: 1065.26018
E. Liflyand and R. Trigub, Conditions for the absolute convergence of Fourier integrals, J. Approx. Theory, 163 (2011), 438–459.
Mathematical Reviews (MathSciNet): MR2775139
Zentralblatt MATH: 1217.42025
Digital Object Identifier: doi:10.1016/j.jat.2010.11.001
E. Liflyand and R. Trigub, On the Representation of a Function as an Absolutely Convergent Fourier Integral, Trudy Mat. Inst. Steklov, 269 (2010), 153–166 (Russian). - English transl.: Proc. Steklov Inst. Math., 269 (2010), 146–159.
Mathematical Reviews (MathSciNet): MR2729981
S. G. Samko and G. S. Kostetskaya, Absolute integrability of Fourier integrals, Vestnik RUDN (Russian Peoples Friendship Univ.), Math., 1 (1994), 138–168.
E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970.
Mathematical Reviews (MathSciNet): MR290095
R. M. Trigub, Absolute convergence of Fourier integrals, summability of Fourier series, and polynomial approximation of functions on the torus, Izv. Akad. Nauk SSSR, Ser.Mat., 44 (1980), 1378–1408 (Russian). - English transl.: Math. USSR Izv., 17 (1981), 567–593.
Mathematical Reviews (MathSciNet): MR603581
Zentralblatt MATH: 0459.42019
R. M. Trigub and E. S. Belinsky, Fourier Analysis and Appoximation of Functions, Kluwer, 2004.
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