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,^[1][2] seorang matematikawan dan fisikawan asal Italia. Stefan Banach, matematikawan asal Polandia, sering kali dianggap sebagai pengasas analisis fungsional modern.^[3]

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)
• Banach S. Theory of Linear Operations Diarsipkan 2021-10-28 di Wayback Machine.. 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

Pranala luar

• Hazewinkel, Michiel, ed. (2001) [1994], "Functional analysis", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
• 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 Diarsipkan 2017-04-01 di Wayback Machine. from University of Colorado Colorado Springs

1. Lawvere, F. William. "Volterra's functionals and covariant cohesion of space" (PDF). acsu.buffalo.edu. Proceedings of the May 1997 Meeting in Perugia. Parameter |url-status= yang tidak diketahui akan diabaikan (bantuan)
2. History of Mathematical Sciences. WORLD SCIENTIFIC. October 2004. hlm. 195. ISBN 978-93-86279-16-3.
3. "Stefan Banach | Polish mathematician". Encyclopedia Britannica (dalam bahasa Inggris). Diakses tanggal 2021-10-24.