Content deleted Content added
Link suggestions feature: 3 links added. |
|||
Line 125:
:<math>\mathcal{L}_k B_m = \frac{1}{k^m}B_m</math>
It is the fact that the eigenvalues <math>k^{-m}<1</math> that marks this as a [[dissipative system]]: for a non-dissipative [[measure-preserving dynamical system]], the eigenvalues of the transfer operator lie on the [[unit circle]].
One may construct a function obeying the multiplication theorem from any [[totally multiplicative function]]. Let <math>f(n)</math> be totally multiplicative; that is, <math>f(mn)=f(m)f(n)</math> for any integers ''m'', ''n''. Define its [[Fourier series]] as
:<math>g(x)=\sum_{n=1}^\infty f(n) \exp(2\pi inx)</math>
| |||