Analisis fungsional

Analisis fungsional adalah suatu cabang matematika (khususnya analisis) yang mengkaji ruang vektor topologis dan pemetaannya. Dalam kajian ini, analisis, topologi, dan aljabar saling bertaut. Tujuan penyelidikan analisis fungsional adalah untuk menemukan aturan abstrak dari bidang-bidang tersebut, yang kemudian dapat diterapkan untuk berbagai masalah konkrit.

Akar sejarah analisis fungsional dapat dilacak dari kajian ruang fungsi khususnya transformasi fungsi seperti transformasi Fourier, dan kajian persamaan diferensial. Penggunaan istilah fungsional berasal dari kalkulus variasi, untuk menandakan fungsi yang argumennya adalah fungsi. Konsep umum fungsional diperkenalkan pada tahun 1887 oleh Vito Volterra, seorang matematikawan dan fisikawan asal Italia. Stefan Banach, matematikawan asal Polandia, sering kali dianggap sebagai pengasas analisis fungsional modern.

 Bacaan lanjutan 

 Aliprantis, C.D., Border, K.C.: Infinite Dimensional Analysis: A Hitchhiker's Guide, 3rd ed., Springer 2007, . Online  (by subscription)
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 Brezis, H.: Analyse Fonctionnelle, Dunod  or 
 Conway, J. B.: A Course in Functional Analysis, 2nd edition, Springer-Verlag, 1994, 
 Dunford, N. and Schwartz, J.T.: Linear Operators, General Theory, John Wiley & Sons, and other 3 volumes, includes visualization charts
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 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
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 Hutson, V., Pym, J.S., Cloud M.J.: Applications of Functional Analysis and Operator Theory, 2nd edition, Elsevier Science, 2005, 
 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, 
 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, 
 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
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 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

 Referensi 

 Pranala luar 


 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  from University of Colorado Colorado Springs