- #1

marcus

Science Advisor

Gold Member

Dearly Missed

- 24,757

- 790

**in math, what is sometimes meant by "Analysis"**

not that "Mathematical Atlas" is the greatest, it provides a rough indication of conventional university-level math-speak, and its welcome page lists these subheadings under "Analysis"

Functional Analysis

Real A.

Complex A.

Differential Equations

Numerical A.

At upperdivision or grad level, unless specified otherwise or modified, the term "Analysis" refers mostly to Functional A. To get more specific, exerpting the Math Atlas, Functional Analysis means things like:

"Function spaces, ...(infinite-dimensional) vector spaces with some kind of metric or other structure, including ring structures (Banach algebras and C-* algebras for example)...

Fourier analysis...

Abstract harmonic analysis...

Integral transforms ...The general theory of transformations between function spaces is part of Functional Analysis... Also includes convolution operators and operational calculi.

Operator theory studies transformations between the vector spaces studied in Functional Analysis, such as differential operators or self-adjoint operators...."

For some reason Math Atlas does not mention Measure Theory as part of Analysis----measures on other structures besides the familiar real line and such.

Math Atlas isnt perfect but it does give a quickanddirty idea of what many people mean by "Analysis"----i.e. Functional Analysis.

Wikipedia probably gives a similar perspective, I havent looked.