Titchmarsh Theorem and its Generalization for the Bessel type transform

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2021 by IJMTT Journal
Volume-67 Issue-4
Year of Publication : 2021
Authors : Balasaheb Bhagaji Waphare,Yashodha Sanjay Sindhe
  10.14445/22315373/IJMTT-V67I4P505

MLA

MLA Style: Balasaheb Bhagaji Waphare,Yashodha Sanjay Sindhe  "Titchmarsh Theorem and its Generalization for the Bessel type transform" International Journal of Mathematics Trends and Technology 67.4 (2021):26-30. 

APA Style: Balasaheb Bhagaji Waphare,Yashodha Sanjay Sindhe(2021). Titchmarsh Theorem and its Generalization for the Bessel type transform International Journal of Mathematics Trends and Technology, 26-30.

Abstract
In this paper we obtain a generalization of Titchmarsh's Theorem for the Bessel type transform for functions satisfying the U - Bessel type Lipschitz condition in Lz,a,b(R) by using a generalized translation operator.

Reference

[1] V.A.Abilov and F.V.Abilova, Approximation of Functions by Fourier-Bessel sums, Izv. Vyssh, Uchebn Zaved, Mat;No.8,3-9(2001).
[2] V.A.Abilov, F.V.Abilova and M.K.Kerimov, On Estimates for the Fourier- Bessel Integral Transform in the L2(R+), Vol.49,No.7(2009).
[3] M.El.Hamma,and R.Daher, Generalization of Titchmansh's Theorem for the Bessel transform,Romanian Journal of Mathematics and Computer Science, Vol.2, No.2,17-22(2012).
[4] I.A.Kipriyanov, Singular Elliptic value problems,[in Russian],Nauka, Moscow(1997).
[5] B.M.Levitan, Expansion in Fourier series and integrals over Bessel, Uspekhi Mat. Nauk,6.No.2,102- 143(1951).
[6] K.Trimeche,Transmutation operators and mean periodic functions associated with di erential operators, Math.Rep.4,No.1,1-282(1988).
[7] E.C.Titchmarsh, Introduction to the theory of Fourier Integrals, Claredon, Oxford, 1948,Komkniga, Moscow,2005.
[8] A.L.Zayed,Handbook of Function and Generalized function transformations,(CRC,Boca Raton, 1996) 5

Keywords : Bessel type operator, Bessel type transform, generalized translation operator, Bessel type function.