Mathematical  Culture and Thought

Mathematical Culture and Thought

From Linear Functional Analysis to Nonlinear Functional Analysis‎: ‎An Interview with Professor Jafar Zafarani

Document Type : Review

Authors
1 Faculty of Mathematics and Statistics‎, ‎University of Isfahan‎, ‎Iran
2 Department of Mathematics‎, ‎University of Zanjan‎, ‎Iran
Abstract
Functional analysis was an  important development in the viewpoint of mathematicians in examining the behavior of functions as a set (space of functions). The important concept of single space and the distance of its points, invented by ‎Fréchet‎ in the early 20th century, and the fusion of algebraic and topological concepts eventually led to the establishment of this branch of mathematics around 1933. The first Iranian mathematician to make a mark in this field was Heydar Radjavi, who contributed to the field in Iran from 1963 to 1968. Another branch of this field is called nonlinear functional analysis, and Behzad Djafari-Rouhani was the first specialist in this branch who worked in the country from 19‎87‎ onwards. Another key figure in the development and expansion of this branch in the country is Jafar Zafarani. This article, after outlining the history of functional analysis, will provide a brief overview of his contributions to this field. Through a conversation with him, we will delve into his experiences and insights from various aspects of his professional life.
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[1] امینی، سید مسعود؛ پورمحمد، حسن، مروری بر تاریخچۀ آنالیز تابعی، فرهنگ و اندیشۀ ریاضی، ۶۸ (۱۴۰۰)،
.۱۷۱ −۱۵۷
[2] امینی هرندی، علیرضا، نظریۀ نقطۀ ثابت نگاشت های ناافزا: پرسش ها و یافته‌ها، فرهنگ و اندیشۀ ریاضی، ۶۷ (۱۳۹۹)،
.۱۷۹ −۱۵۷
[3] برزیس، حییم، آنالیز تابعی؛ نظریه و کاربردها، ج ۱، ترجمۀ بهزاد جعفری روحانی، مرکز انتشارات علمی دانشگاه
 آزاد اسلامی، تهران،  ۱۳۷۶
[4] جعفری روحانی، بهزاد، نگاشتهای انبساطی، مسئلۀ نیرنبرگ و نظریۀ ارگودیک انتشارات دانشگاه شهید بهشتی، تهران، ۱۳۸۴
[5]رجبعلی پور، مهدی، با کاروان حله، فرهنگ و اندیشۀ ریاضی، ۶۴ (۱۳۹۸)، ۱-۱۶
[6] صال مصلحیان، محمد؛ اسماعیل زاده، محمد، استفان باناخ، فرهنگ و اندیشۀ ریاضی، ۳۸  (۱۳۸۶)، ۶۷-۷۴
[7]مقصودی، سعید، دکتر محمود لشکری زاده بمی: زندگی و آثار، ریاضی و جامعه، ۱ (۱۴۰۰)، ۱-۲۶
[8] مقصودی، سعید، سیری در آنالیز فوریه: گفت وگویی با دکتر مهدی هرمزی، فرهنگ و اندیشۀ ریاضی، ۷۲ (۱۴۰۲)، ۱-۴۶
[9] Bacak, M., Convex Analysis and Optimization in Hadamard Spaces in Nonlinear
Analysis and Applications, vol. 22, De Gruyter, Berlin, 2014.
[10] Bernkopf, Michael, The development of function spaces with particular reference to their origins
in integral equation theory, Arch. History Exact Sci., 3 (1966), 1-96.
[11] Birkhoff, G., Kreyszig, E., The establishment of functional analysis, Historia Math., 11 (1984),
no.3, 258–321.
[12] Browder, F. E., The relation of functional analysis to concrete analysis in 20th century mathematics,
Historia Math., 2 (1975), 577–590.
[13] Dieudonné, J., History of Functional Analysis, North-Holland Math. Stud., vol. 49, North-Holland
Publishing Co., Amsterdam-New York, 1981.
[14] Miyadera, I., Nonlinear Semigroups, Transl. Math. Monogr., vol. 109, American Mathematical
Society, Providence, RI, 1992.
[15] Pier, Jean-Paul, Mathematical Analysis During the 20th Century, Oxford University Press, New
York, 2001.
[16] Schwartz, Jacob T., Non-Linear Functional Analysis, Gordon & Breach Science Pub., New York,
1969.
[17] Smithies, Frank, The shaping of functional analysis. Bull. London Math. Soc., 29 (1997), no.2,
129-138.
[18] Zeidler, E., Nonlinear Functional Analysis and its Applications, I, Fixed-point Theorems, 1986.
[19] Zeidler, E., Nonlinear Functional Analysis and its Applications, II/B, Nonlinear Monotone Operators,
Springer-Verlag, New York, 1990.

  • Receive Date 03 April 2024
  • Revise Date 04 May 2024
  • Accept Date 04 May 2024
  • Publish Date 22 July 2024