Functional analysis
Functional analysis is a branch of mathematical analysis.[1][2] This area emerged from the studies of differential equations (especially partial differential equations[3]). It has many applications in various fields.[4][5][6] One of the famous use is numerical analysis.[7][8][9][10]
Functional Analysis Media
One of the possible modes of vibration of an idealized circular drum head. These modes are eigenfunctions of a linear operator on a function space, a common construction in functional analysis.
References
- ↑ Kantorovich, L. V., & Akilov, G. P. (1982). Functional Analysis Pergamon Press. University of Michigan.
- ↑ Deimling, K. (2010). Nonlinear functional analysis. Courier Corporation.
- ↑ Brezis, H. (2010). Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer Science & Business Media.
- ↑ Zeidler, E., Nonlinear Functional Analysis and Its Applications I-V. Springer Science & Business Media.
- ↑ Zeidler, E. (2012). Applied functional analysis: main principles and their applications. Springer Science & Business Media.
- ↑ Zeidler, E. (2012). Applied functional analysis: applications to mathematical physics. Springer Science & Business Media.
- ↑ Collatz, L. (2014). Functional analysis and numerical mathematics. Academic Press
- ↑ Computational Functional Analysis 2nd Edition, Ramon Moore & Michael Cloud (2007), Woodhead Publishing.
- ↑ Lebedev, V. I. (2000). Functional analysis and computational mathematics. Moscow: Fizmatlit.
- ↑ M. Nakao, M. Plum, Y. Watanabe (2019) Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations (Springer Series in Computational Mathematics).
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 (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
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Quotations from Wikiquote |
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Textbooks from Wikibooks |
- 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