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.

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).

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

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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

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[1] Kantorovich, L. V., & Akilov, G. P. (1982). Functional Analysis Pergamon Press. University of Michigan.

[2] Deimling, K. (2010). Nonlinear functional analysis. Courier Corporation.

[3] Brezis, H. (2010). Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer Science & Business Media.

[4] Zeidler, E., Nonlinear Functional Analysis and Its Applications I-V. Springer Science & Business Media.

[5] Zeidler, E. (2012). Applied functional analysis: main principles and their applications. Springer Science & Business Media.

[6] Zeidler, E. (2012). Applied functional analysis: applications to mathematical physics. Springer Science & Business Media.

[7] Collatz, L. (2014). Functional analysis and numerical mathematics. Academic Press

[8] Computational Functional Analysis 2nd Edition, Ramon Moore & Michael Cloud (2007), Woodhead Publishing.

[9] Lebedev, V. I. (2000). Functional analysis and computational mathematics. Moscow: Fizmatlit.

[10] M. Nakao, M. Plum, Y. Watanabe (2019) Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations (Springer Series in Computational Mathematics).

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Functional analysis

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