Background
In 1903, Fredholm invented the concept of pseudo inverse for integral operators, then around half a decade later mathematicians came up with the idea of pseudo inverse for matrix.
On the internet plenty of information is available regarding the latter, stating that a pseudo inverse matrix is defined as the unique matrix satisfying the Moore–Penrose conditions - four basic properties of an inverse matrix in usual sense.
Unfortunately, there are not many (free) sources online that explain Fredholm pseudo inverse of integral operators.
My Questions
- What is Fredholm pseudo inverse? Answers in your own words or providing online references are both welcomed.
- Is Fredholm pseudo inverse defined in a similar fashion as in the definition of matrix pseudo inverse?
- What is the Fredholm pseudo inverse, if exist, of the operator $$\int^b_a $$?
- What are some applications of Fredholm pseudo inverse?