K-functional related to the Deformed Hankel Transform

Rakhimi, Larbi; Khadari, Abdelmajid; Daher, Radouan

doi:10.2478/aupcsm-2023-0002

Abstract

The main result of the paper is the proof of the equivalence theorem for a K-functional and a modulus of smoothness for the Deformed Hankel Transform. Before that, we introduce the K-functional associated to the Deformed Hankel Transform.

References

Al Subaie, Reem Fahad, and Mohamed Ali Mourou. “Equivalence of K-Functionals and Modulus of Smoothness Generated by a Generalized Dunkl Operator on the Real Line.” Adv. Pure Math. 5, no. 6 (2015): 367-376. Cited on 13.
Search in Google Scholar Back to article
Belkina, E. S., and Sergeĭ Sergeevich Platonov. “Equivalence of K-functionals and modulus of smoothness constructed by generalized Dunkl translations.” Russian Math. (Iz. VUZ) 52, no. 8 (2008): 1-11. Cited on 13.
Search in Google Scholar Back to article
Ben Saïd, Salem. “A product formula and a convolution structure for a k-Hankel transform on ℝ.” J. Math. Anal. Appl. 463, no. 2 (2018): 1132-1146. Cited on 15.
Search in Google Scholar Back to article
Ben Saïd, Salem, and Luc Deleaval. “Translation operator and maximal function for the (k,1)-generalized Fourier transform. J. Funct. Anal. 279, no. 8 (2020): Art. no. 108706. Cited on 15.
Search in Google Scholar Back to article
Ben Saïd, Salem, Toshiyuki Kobayashi, and Bent Ørsted. “Laguerre semigroup and Dunkl operators.” Compos. Math. 148, no. 4 (2012): 1265-1336. Cited on 15.
Search in Google Scholar Back to article
Ben Saïd, Salem, Mohamed Amine Boubatra, and Mohamed Sifi. “On the deformed Besov-Hankel spaces.” Opuscula Math. 40, no. 2 (2020): 171-207. Cited on 15.
Search in Google Scholar Back to article
Boubatra, Mohamed Amine. “On the generalized Dunkl Dini-Lipschitz spaces.” Integral Transforms Spec. Funct. 33, no. 10 (2022): 782-798. Cited on 16.
Search in Google Scholar Back to article
El Hamma, Mohamed, and Radouan Daher. “Equivalence of K-functionals and modulus of smoothness constructed by generalized Jacobi transform.” Integral Transforms Spec. Funct. 30, no. 12 (2019): 1018-1024. Cited on 13.
Search in Google Scholar Back to article
Negzaoui, Selma, and Sara Oukili. “Modulus of continuity and modulus of smoothness related to the deformed Hankel transform.” Results Math. 76, no. 3 (2021): Paper No. 164. Cited on 14, 15, 16 and 19.
Search in Google Scholar Back to article
Rakhimi, Larbi, and Radouan Daher. “Equivalence of K-functionals and modulus of smoothness for Laguerre type operator.” J. Pseudo-Differ. Oper. Appl. 12, no. 4 (2021): Paper No. 53. Cited on 13.
Search in Google Scholar Back to article
Rakhimi, Larbi, and Radouan Daher. “Modulus of smoothness and K-functionals constructed by generalized Laguerre-Bessel operator.” Tatra Mt. Math. Publ. 81 (2022): 107-116. Cited on 13.
Search in Google Scholar Back to article
Watson, George Neville. A Treatise on the Theory of Bessel Functions. 2nd ed. reprinted. Springer Monographs in Mathematics. New York: Cambridge University Press, 1966. Cited on 17.
Search in Google Scholar Back to article

K-functional related to the Deformed Hankel Transform

Abstract

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