Functional analysis

branch of mathematical analysis concerned with infinite-dimensional topological vector spaces, often spaces of functions

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].


  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).

Further readingEdit

  • 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 websitesEdit