Convergence of Fourier series, and generalised functions Flashcards
1
Q
Define a δ-convergent sequence.
A
2
Q
Define the Dirac delta function δ(x).
A
3
Q
Define a piecewise continuous function.
A
4
Q
Define a piecewise smooth function.
A
5
Q
Define a test function.
A
6
Q
Define when two generalised functions g(x) and h(x) are said to be equal?
A
7
Q
What is the integral of f(x), and some, as yet unspecified, function g’(x)?
A
8
Q
Show the following.
A
9
Q
Show the following.
A
10
Q
Show the following.
A
11
Q
Show the following.
A
12
Q
Show the following.
A
13
Q
What is the general method for proving identities of generalised functions?
A
Integrate both sides of the proposed identity with respect to an arbitrary test function f ∈ K to show equality.
