A modified and a finite index Weber transforms (Q699301)

Finite and infinite integral transformations with respect to an index of Bessel functions in the kernel are studied. The considered transforms have some relationship with the known Weber transform. The authors investigate operational properties of these transformations and apply them to various problems in differential equations with non-constant coefficients. The main theorems are proved, which describe the image of some spaces of square integrable functions with respect to a measure under these transforms.