are there non-connstant function that satisfy the following asumptions ??(adsbygoogle = window.adsbygoogle || []).push({});

[tex] y(x)=y(kx) [/tex] they are 'periodic' but under DILATIONS

and also satisfy the differential equation of the form (eigenvalue problem)

[tex] axy'(x)+bx^{2}y''(x)=e_{n}y(x) [/tex]

if the Lie Group is of translations [tex] y(x+1)=y(x) [/tex] we may have sine and cosine , however for the case of DILATIONS i do not know what functions can we take.

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# Periodic functions (or similar)

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