An integral equation
Published online by Cambridge University Press: 24 October 2008
Extract
1. The integral equation
where 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 that
Then, if we integrate repeatedly by parts, and write z for fp (x), (1·1) becomes
The only solutions are finite combinations of exponentials.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 28 , Issue 2 , April 1932 , pp. 165 - 173
- Copyright
- Copyright © Cambridge Philosophical Society 1932
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