Functional Analysis Seminar

Question 1

Define the kernel over a set X.

Answer 1

Question 2

List the properties of an inner product.

Answer 2

Question 3

Given an orthonormal basis, write down the Fourier Coefficients and Bessel’s Inequality.

Answer 3

Question 4

Write down Riesz’s Representation of an element x.

Answer 4

Question 5

Question 6

Define the direct sum of Hilbert Spaces, and its inner product.

Answer 6

Question 7

Define the tensor product of Hilbert Spaces.

Answer 7