Geodesic
Titchmarsh's theorem of Hankel transform
Daghestan Electronic Mathematical Reports, Tome 11 (2019), pp. 11-24.

Voir la notice de l'article provenant de la source Math-Net.Ru

Hankel transform (or Fourier-Bessel transform) is a fundamental tool in many areas of mathematics and engineering, including analysis, partial differential equations, probability, analytic number theory, data analysis, etc. In this article, we prove an analog of Titchmarsh's theorem for the Hankel transform of functions satisfying the Hankel-Lipschitz condition.
Mots-clés : Hankel transform, Titchmarsh theorem, Generalized derivatives in the sense of Levi. 
@article{DEMR_2019_11_a1,
     author = {Boudref Mohamed-Ahmed},
     title = {Titchmarsh's theorem of {Hankel} transform},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {11--24},
     publisher = {mathdoc},
     volume = {11},
     year = {2019},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/DEMR_2019_11_a1/}
}
TY  - JOUR
AU  - Boudref Mohamed-Ahmed
TI  - Titchmarsh's theorem of Hankel transform
JO  - Daghestan Electronic Mathematical Reports
PY  - 2019
SP  - 11
EP  - 24
VL  - 11
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/DEMR_2019_11_a1/
LA  - en
ID  - DEMR_2019_11_a1
ER  - 
%0 Journal Article
%A Boudref Mohamed-Ahmed
%T Titchmarsh's theorem of Hankel transform
%J Daghestan Electronic Mathematical Reports
%D 2019
%P 11-24
%V 11
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/DEMR_2019_11_a1/
%G en
%F DEMR_2019_11_a1
Boudref Mohamed-Ahmed. Titchmarsh's theorem of Hankel transform. Daghestan Electronic Mathematical Reports, Tome 11 (2019), pp. 11-24. https://geodesic-test.mathdoc.fr/item/DEMR_2019_11_a1/

[1] Daher R. and Hamma M., “An analog of Titchmarch's theorem of Jacobi transform”, Int. J. Math. Anal., 6:17–20 (2012), 975–981 | Zbl

[2] Ditkine V., “Calcul opérationnel”, UMN, 2:6(22) (1947), 72–158

[3] Ditkine V., “Calcul opérationnel”, UMN, 2:6(22) (1947), 72–158

[4] Kantorovitch L., “On approximate calculation of certain types of definite integrals and other applications of the method of selection of singularities”, Mat. Sb., 41 (1934), 235–245

[5] James J. F., A Student's guide to Fourier transform with applications in Physics and Engineering, Third edition, Cambridge University Press, 2011

[6] Kikushi H., “Bessel transforms”, Bull. Electrot. Lab., 16 (1954), 111–120

[7] Lébedev N., Certaines transformations intégrales de la physique mathématique, 1950

[8] Maslouhi M., “An analog of Titchmarsh's theorem for Dunkl transform”, Integral transfomrs and Spec. Functions, 21:9-10 (2010), 771–778 | DOI | Zbl

[9] Nikol'skii S. M., Approximation of functions of several variables and imbedding and theorems, Springer-Verlag, New York, 2011

[10] Platonov S. S., “An analog of Titchmarsh's theorem of the Fourier-walsh transform”, Mathematical notes, 103:1 (2018), 96–103 | DOI | Zbl

[11] Titchmarsh E. C., Introduction to the theory of Fourier integrals, Oxford University Press, Amen House, London, 1948

[12] Zygmund A., Trigonometric series, Cambridge University Press, London, 1968