Functional analysis

Functional analysis is that branch of mathematics and specifically of analysis which is concerned with the study of spaces of functions. It has its historical roots in the study of transformations such as the Fourier transform and in the study of differential and integral equations. The word 'functional' goes back to the calculus of variations, implying a function whose argument is a function. Its use in general has been attributed to Volterra.

References

• Yosida, K.: Functional Analysis, Springer-Verlag, 6th edition, 1980
• Schechter, M.: Principles of Functional Analysis, AMS, 2nd edition, 2001
• Hutson, V., Pym, J.S., Cloud M.J.: Applications of Functional Analysis and Operator Theory, 2nd edition, Elsevier Science, 2005, ISBN 0444517901
• Dunford, N. and Schwartz, J.T. : Linear Operators, General Theory, and other 3 volumes, includes visualization charts
• Brezis, H.: Analyse Fonctionnelle, Dunod
• Sobolev, S.L.: Applications of Functional Analysis in Mathematical Physics, AMS, 1963
• Lebedev, L.P. and Vorovich, I.I.: Functional Analysis in Mechanics, Springer-Verlag, 2002