Functional analysis

Functional analysis is a branch of mathematical analysis. This area emerged from the studies of differential equations (especially partial differential equations). It has many applications in various fields. One of the famous use is numerical analysis.

Further reading

• Aliprantis, C.D., Border, K.C.: Infinite Dimensional Analysis: A Hitchhiker's Guide, 3rd ed., Springer 2007, ISBN 978-3-540-32696-0. Online doi:10.1007/3-540-29587-9 (by subscription)
• Bachman, G., Narici, L.: Functional analysis, Academic Press, 1966. (reprint Dover Publications)
• Banach S.: Theory of Linear Operations. Volume 38, North-Holland Mathematical Library, 1987, ISBN 0-444-70184-2
• Brezis, H.: Analyse Fonctionnelle, Dunod ISBN 978-2-10-004314-9 or ISBN 978-2-10-049336-4
• Conway, J. B.: A Course in Functional Analysis, 2nd edition, Springer-Verlag, 1994, ISBN 0-387-97245-5
• Dunford, N. and Schwartz, J.T.: Linear Operators, General Theory, John Wiley & Sons, and other 3 volumes, includes visualization charts
• Edwards, R. E.: Functional Analysis, Theory and Applications, Hold, Rinehart and Winston, 1965.
• Eidelman, Yuli, Vitali Milman, and Antonis Tsolomitis: Functional Analysis: An Introduction, American Mathematical Society, 2004.
• Friedman, A.: Foundations of Modern Analysis, Dover Publications, Paperback Edition, July 21, 2010
• Giles,J.R.: Introduction to the Analysis of Normed Linear Spaces,Cambridge University Press,2000
• Hirsch F., Lacombe G. - "Elements of Functional Analysis", Springer 1999.
• Hutson, V., Pym, J.S., Cloud M.J.: Applications of Functional Analysis and Operator Theory, 2nd edition, Elsevier Science, 2005, ISBN 0-444-51790-1
• Kantorovitz, S.,Introduction to Modern Analysis, Oxford University Press,2003,2nd ed.2006.
• Kolmogorov, A.N and Fomin, S.V.: Elements of the Theory of Functions and Functional Analysis, Dover Publications, 1999
• Kreyszig, E.: Introductory Functional Analysis with Applications, Wiley, 1989.
• Lax, P.: Functional Analysis, Wiley-Interscience, 2002, ISBN 0-471-55604-1
• Lebedev, L.P. and Vorovich, I.I.: Functional Analysis in Mechanics, Springer-Verlag, 2002
• Michel, Anthony N. and Charles J. Herget: Applied Algebra and Functional Analysis, Dover, 1993.
• Pietsch, Albrecht: History of Banach spaces and linear operators, Birkhäuser Boston Inc., 2007, ISBN 978-0-8176-4367-6
• Reed, M., Simon, B.: "Functional Analysis", Academic Press 1980.
• Riesz, F. and Sz.-Nagy, B.: Functional Analysis, Dover Publications, 1990
• Rudin, W.: Functional Analysis, McGraw-Hill Science, 1991
• Saxe, Karen: Beginning Functional Analysis, Springer, 2001
• Schechter, M.: Principles of Functional Analysis, AMS, 2nd edition, 2001
• Shilov, Georgi E.: Elementary Functional Analysis, Dover, 1996.
• Sobolev, S.L.: Applications of Functional Analysis in Mathematical Physics, AMS, 1963
• Vogt, D., Meise, R.: Introduction to Functional Analysis, Oxford University Press, 1997.
• Yosida, K.: Functional Analysis, Springer-Verlag, 6th edition, 1980

Other websites

• Topics in Real and Functional Analysis by Gerald Teschl, University of Vienna.
• Lecture Notes on Functional Analysis by Yevgeny Vilensky, New York University.
• Lecture videos on functional analysis by Greg Morrow Archived 2017-04-01 at the Wayback Machine from University of Colorado Colorado Springs