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An analogue of the Titchmarsh theorem for the Fourier transform on the group of \(p\)-adic numbers. (English) Zbl 1409.11116
Summary: In this paper, for functions on the group \(\mathbb Q_p\), we prove an analogue of the classical Titchmarsh theorem on description of the image under the Fourier transform of a set of functions satisfying the Lipschitz condition in \(L^2\).

MSC:
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
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References:
[1] E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals (Clarendon Press, Oxford, 1937). · Zbl 0017.40404
[2] Platonov, S. S., The Fourier transform of functions satisfying the Lipschitz condition on rank 1 symmetric spaces 1, Sib. Math. J., 46, 1108-1118, (2005) · Zbl 1150.42307
[3] Younis, M. S., Fourier transform of Lipschitz functions on the hyperbolic plane, Int. J. Math. & Math. Sci., 21, 397-401, (1998) · Zbl 0903.42002
[4] Daher, R.; Hamma, M., An analog of titchmarsh’s theorem of Jacobi transform, Int. J. Math. Anal., 6, 975-981, (2012) · Zbl 1248.33016
[5] Maslouhi, M., An analog of titchmarsh’s theorem for the Dunkl transform, Integ. Transf. Spec. Funct., 21, 771-778, (2010) · Zbl 1216.47057
[6] V. S. Vladimirov, I. V. Volovich and E. I. Zelenov, p-Adic Analysis and Mathematical Physics (World Scientific, Singapore, 1994). · Zbl 0812.46076
[7] Vilenkin, N. Ya.; Rubinshtein, A. I., A theorem of S. B. Stechkin on absolute convergence of a series with respect to systems of characters of zero-dimensional abelian groups, SovietMath. (Izv. VUZ. Matematika), 19, 1-7, (1975)
[8] G. N. Agaev, N. Ya. Vilenkin, G. M. Dzhafarli and A. I. Rubinshtein, Multiplicative Systems of Functions and Harmonic Analysis on Zero-Dimensional Groups (Elm, Baku, 1981) [in Russian]. · Zbl 0588.43001
[9] Rubinshtein, A. I., Moduli of continuity of functions, defined on a zero-dimensional group, Math. Notes., 23, 205-211, (1978) · Zbl 0425.43011
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