Do functions that vanish at the endpoints form a vector space?

L] and that vanish at the end points x = 0 and x = L form a vector space? Answ: Yes.

Are periodic functions vector spaces?

These vectors are all 2π-periodic functions, so they are all in our vector space. As n > 0 they are all non-zero vectors. That these vectors (functions) are a spanning set for a vector space of 2π-periodic functions is Fourier’s Theorem.

Is the sum of two periodic functions always periodic?

Unlike the continuous case, given two discrete periodic signals, their sum is always periodic. We give a characterization for the period of the sum; as shown, the least common multiple of the periods of the signals being added is not necessarily the period of the sum.

Are periodic functions closed under addition?

Then f,g are periodic. So their sum is also. Thus, (f+g)(x+p)=f(x+p)+g(x+p)=f(x)+g(x)=(f+g)(x). So it’s closed under addition.

Can the sum of a periodic function and a non periodic function be periodic?

Yes, it is possible. For example, , satisfy the property. is clearly periodic, and the sum, which is is also periodic.

How do you find the period of two periodic functions?

For example, the function has no period. The function , where is either or and , has a period if and only if is rational for all . If your function satisfies this condition, then here’s how you find its period: Multiply each of these fractions by the least common multiple of their denominators.

Is the sum of 2 periodic functions periodic?

The answer is well known in the case when two nonconstant periodic functions are defined and continuous on the whole real line and the operation is addition. In this case the sum is periodic if and only if the periods of summands are commensurable.

Is the sum of 2 periodic functions always periodic?

How do you find the period of a function without graphing?

If you look at a graph, you can see that the period (length of one wave) is . Without the graph, you can divide with the frequency, which in this case, is 1.