INTEGRAL TRANSFORMS WITH THE CONFLUENT HYPERDEOMETRIC FUNCTION OF KUMMER AND THE CUT BESSEL FUNCTION IN THE KERNELS AND INTEGRAL EQUATIONS OF THE FIRST KIND IN THE SPACE OF SUMMABLE FUNCTIONS
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Abstract
Three integral transforms involving confluent hyperdeometric function of Kummer and the cut Bessel function in the kernels are studied on the spaces of p- summable functions on a finite interval [a,b] of the real line. Mapping properties such as the boundedness, the range of the considered transform are given, and the inversion formulas are established. Three integral equations of the first kind with the confluent hyperdeometric function of Kummer and the cut Bessel function in the kernels also are considered. The solutions of the investigating equations in the closed form are established, and conditions for its solvability in the space of summable functions are given. The results generalize the well know findings for corresponding integral equations.
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References
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