Author:
Hardy G. H.,Titchmarsh E. C.
Abstract
1. The integral equationwhere x, f (x), and λ are real and α positive, may be regarded as a differential equation of order α. Suppose for example that α is a positive integer p, that f (x) tends to 0, when x → ∞, with sufficient rapidity, and thatThen, if we integrate repeatedly by parts, and write z for fp (x), (1·1) becomesThe only solutions are finite combinations of exponentials.
Publisher
Cambridge University Press (CUP)
Reference4 articles.
1. Solution of certain integral equations considered by Bateman, Kapteyn, Littlewood and Milne;Hardy;Proc. London Math. Soc.,1924
2. On Abel's Integral Equation and Fractional Integrals
3. Über eine Klasse singulärer Integralgleichungen;Bochner;Berliner Sitzungsberichte,1930
4. On Mellin's inversion formula;Hardy;Messenger of Math.,1918
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