Purchase Solution

# Fourier Series - Uniform and Pointwise Convergence Problem

Not what you're looking for?

Please see the attached file for the f(x) function.

a) On the interval [a,b], does the sequence of functions converge pointwise? If yes, what is the limit function? Is the convergence uniform?

b) Answer the same three questions, but now let the function be defined on the real line.

##### Solution Summary

Uniform an pointwise convergence of a Fourier Series is investigated on an interval and across the entire real line.

##### Solution Preview

fn(x)=0 if x<=n and fn(x)=x^2-n^2 if x>=n
(a) On the interval [a,b], fn(x) converges pointwise, then limit function is g(x)=0. The convergence is uniform.
Proof: For any e>0, we can find enough ...

##### Probability Quiz

Some questions on probability

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.