Index transforms associated with Bessel and Lommel functions (Q1848658)

The author extends a variety of index transforms with Bessel and Lommel functions as kernels by considering mapping properties of the related integral operators. The integral representations of the considered kernels are deduced. Boundedness properties of Lommel and Bessel function transforms are discussed. Parseval equalities, Plancherel type theorems and inversion formulas are also given. Actually this work is in continuation of the author's previous works, interested research workers of this field may also see the following monograph and papers of the author: Index transforms (1996; Zbl 0845.44001); J. Comput. Appl. Math. 85, No. 1, 169-179 (1997; Zbl 0886.44003); ibid. 118, No. 1-2, 353-361 (2000; Zbl 0959.44005).