Abstract
AbstractIt is known [Herman Weyl, 1910] that every linear second-order differential expression L (with real coefficients) is such that Ly = λy (im λ ≠ 0) has at least one solution belonging to the class L2 = L2[0, ∞) of functions, the squares of whose moduli are Lebesgue-integrable on [0, ∞). This celebrated result was later proved by E. C. Titchmarsh (1940–1944), using sophisticated analysis of bilinear transformation. The aim of the present note is to prove the same result once again, but using only elementary analysis and school geometry. The power of this method will be appreciated further when one realises the amount of simplifications that can be acheived by this expressions. This part of the note course will be taken up in a subsequent paper.
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Schedule a callMore From: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
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