Where can I find challenging functional analysis problems for self-study?

In summary, the conversation discusses recommendations for finding good functional analysis problems. One person suggests GTM books such as Conway and Pedersen, but another mentions that Pedersen's problems may be too challenging for a first course. The last person mentions purchasing Exercises in Functional Analysis by Costara and Popa for self-study purposes.
  • #1
maze
662
4
Does anyone know of where I should look to find lots of good functional analysis problems? I am currently reading Kreyszig which has great commentary, but the majority of the exercises are simple.
 
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  • #2
There are lots of good GTM books with challenging problems, e.g. Conway and Pedersen. In my opinion Pedersen's problems are too challenging, in the sense that it's almost impossible to do most of them if this is your first functional analysis course.
 
  • #3
Thanks. I'm going to take your advice and buy Conway.
 
  • #4
I just picked up Exercises in Functional Analysis by Costara and Popa. This will be invaluable for me, since I'm self-studying, so its always nice to be able to check my work if I get stuck.
 

1. What is functional analysis?

Functional analysis is a branch of mathematics that deals with the study of vector spaces and linear transformations. It focuses on the structure and properties of these spaces and transformations, and their applications in various areas such as physics, engineering, and economics.

2. What are some common examples of functional analysis problems?

Some common examples of functional analysis problems include finding eigenvalues and eigenvectors of linear transformations, solving differential equations using functional analytic techniques, and studying the convergence and stability of numerical algorithms.

3. How is functional analysis used in other fields?

Functional analysis has various applications in other fields such as physics, engineering, economics, and computer science. For example, it is used in quantum mechanics to study the behavior of particles, in control theory to design optimal control systems, and in data analysis to understand complex datasets.

4. What are some important concepts in functional analysis?

Some important concepts in functional analysis include normed vector spaces, Banach spaces, Hilbert spaces, linear operators, and spectral theory. These concepts are essential for understanding the structure and properties of functional spaces and for solving problems in various applications.

5. What are some techniques used to solve functional analysis problems?

Some commonly used techniques in functional analysis include the spectral theorem, the Hahn-Banach theorem, the Banach fixed-point theorem, and the Riesz representation theorem. These techniques provide powerful tools for solving a wide range of problems and for proving important results in functional analysis.

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