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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 Eidelman, Yuli, Vitali Milman, and Antonis Tsolomitis: Functional Analysis: An Introduction, American Mathematical Society, 2004.
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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