daveb said:I always though Kreyszig's book was outstanding.
bugatti79 said:Yes, I have that. Its still a bit abstract...:-)
homeomorphic said:Robert Geroch, Mathematical Physics. Last 2 chapters. Best intro to functional I have seen. I don't know about worked examples. There are some very good examples, but also very nice proofs.
The point of functional might be to be abstract, but the word abstract is a verb. Things should be abstracted FROM something. Unfortunately, I'm not aware of any functional analysis book that keeps that in mind quite as much as they ought to, except maybe Dieudonne's History of Functional Analysis, but it is not very complete or readable.
Functional analysis is a branch of mathematics that studies vector spaces and linear transformations between them. It is used to analyze the properties and behavior of functions in a mathematical framework.
Functional analysis is commonly used in fields such as physics, engineering, and economics to model and analyze physical systems, structures, and processes. It is also used in computer science to study algorithms and data structures.
One example of functional analysis is the Fourier transform, which is used to decompose a complex signal into simpler components. Another example is the Laplace transform, which is used to solve differential equations.
Some key concepts in functional analysis include Banach spaces, Hilbert spaces, and linear operators. Other important topics include topological vector spaces, normed spaces, and dual spaces.
Some common techniques used in functional analysis include the Hahn-Banach theorem, the Baire category theorem, and the open mapping theorem. Other techniques include spectral theory, convex analysis, and the application of functional analysis to differential equations.