Recent content by Hermes10

Dear all, I am wondering why the Fourier Series converges at a finite discontinuity of a periodic function at 1/2*(y1+y2) at the point f(x1), where x1 is the point at which the discontinuity occurs and y1 is the limiting value for the function when we approach x=x1 from one side and y2 is the...

Hello, I was doing problem involving Fourier Series and came across the Dirichlet conditions which say among others that the function has to be single valued in order to be able to use Fourier Series to describe it. What does it mean for a function to be single valued? Hermes10

Mhm, well, I suppose your previous comment proved that if L(x) has a well defined parity, then there are even and odd solutions to that equation. It indeed does not say the other way round, that is if there are even and odd solutions, the L(x) has then a well defined parity. To be honest with...

Yeah, I think my mistake is to infer too much from what is given. But say I am given a function that does not have a well defined parity. Does this mean that it may or may not have even or odd functions as solution?

Does it mean that a differential equation has even and odd solutions if and only if the parity of the equation is well-defined?