Analisis fungsional: Perbedaan antara revisi
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'''Analisis Fungsional''' adalah suatu cabang [[matematika]] (khususnya [[Analisis matematis|analisis]]) yang mempelajari [[ruang vektor topologis]] dan pemetaannya. Dalam kajian ini, analisis, topologi, dan aljabar saling bertaut. Akar sejarah analisis fugsional 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, {{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)
* [[Stefan Banach|Banach S.]] [http://www.ebook3000.com/Theory-of-Linear-Operations--Volume-38--North-Holland-Mathematical-Library--by-S--Banach_134628.html ''Theory of Linear Operations'']. Volume 38, North-Holland Mathematical Library, 1987, {{ISBN|0-444-70184-2}}
* [[Haïm Brezis|Brezis, H.]]: ''Analyse Fonctionnelle'', Dunod {{ISBN|978-2-10-004314-9}} or {{ISBN|978-2-10-049336-4}}
* [[John B. Conway|Conway, J. B.]]: ''A Course in Functional Analysis'', 2nd edition, Springer-Verlag, 1994, {{ISBN|0-387-97245-5}}
* [[Nelson Dunford|Dunford, N.]] and [[Jacob T. Schwartz|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.
* [[Avner Friedman|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|Kolmogorov, A.N]] and [[Sergei Fomin|Fomin, S.V.]]: ''Elements of the Theory of Functions and Functional Analysis'', Dover Publications, 1999
* [[Erwin Kreyszig|Kreyszig, E.]]: ''Introductory Functional Analysis with Applications'', Wiley, 1989.
* [[Peter Lax|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}}
* [[Michael C. Reed|Reed, M.]], [[Barry Simon|Simon, B.]]: "Functional Analysis", Academic Press 1980.
* Riesz, F. and Sz.-Nagy, B.: ''Functional Analysis'', Dover Publications, 1990
* [[Walter Rudin|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|Sobolev, S.L.]]: ''Applications of Functional Analysis in Mathematical Physics'', AMS, 1963
* Vogt, D., Meise, R.: ''Introduction to Functional Analysis'', Oxford University Press, 1997.
* [[Kōsaku Yosida|Yosida, K.]]: ''Functional Analysis'', Springer-Verlag, 6th edition, 1980
== Pranala luar ==
{{Sister project links|wikt=no|commons=no|b=Functional Analysis|n=no|q=Functional analysis|s=no|v=no|voy=no|species=no|d=no}}
* {{Springer|title=Functional analysis|id=p/f042020}}
* [https://www.mat.univie.ac.at/~gerald/ftp/book-fa/index.html Topics in Real and Functional Analysis] by [[Gerald Teschl]], University of Vienna.
* [https://web.archive.org/web/20161021093450/http://www.math.nyu.edu/phd_students/vilensky/Functional_Analysis.pdf Lecture Notes on Functional Analysis] by Yevgeny Vilensky, New York University.
* [https://www.youtube.com/playlist?list=PLE1C83D79C93E2266 Lecture videos on functional analysis] by [http://www.uccs.edu/~gmorrow/ Greg Morrow] from [[University of Colorado Colorado Springs]]
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