# Professor S Minakshisundaram

**Subbaramiah Minakshisundaram** was born in Trichur, Kerala on October 12, 1913.

His father was originally from Salem, Tamilnadu (not far away from the birthplace of Ramanujan) and so Minakshisundaram had all his education in Madras. He took his BA (Hons.) in Mathematics from Loyola College in 1934 securing 1st class in the Madras University examination.

Though there was always a strong tradition of scholarship and learning in and around Madras, many brilliant young men of that time used to opt for the more lucrative and prestigious administrative services. But young Minakshisundaram was different; he joined Madras University as a research scholar and started working with Ananda Rau. After taking the DSc degree from Madras University in 1940, Minakshisundaram found himself without a job. Thanks to the timely help of Fr. Racine, who was professor at Loyola College, could earn a living by coaching students for the university examinations.

During these years he and Fr. Racine organised a weekly Mathematics Seminar which attracted many enthusiastic participants like K Chandrasekharan and K G Ramanathan. Fortunately, he got the job of a lecturer at Andhra University in Waltair. In 1944, Marshall H Stone was in Madras and he wanted to meet the best young mathematicians there, especially Minakshisundaram and Chandrasekharan. M H Stone, who was a Professor at Chicago, had a reputation for `discovering' young talents and shaping their career. For both Minakshisundaram and Chandrasekharan this meeting with Stone was a turning point. By the reports of Stone they were ordered a membership at the Institute for Advanced Study in Princeton.

The atmosphere at the Institute gave him a great boost and it was there where Minakshisundaram's best mathematical works were done. He collaborated with the Swedish mathematician Ake Pleijel and wrote his most quoted paper. Minakshisundaram returned to India in 1948 by which time he was internationally recognised for his brilliant work. Early in 1950 Andhra University promoted him to full professorship in Mathematical Physics. Soon after he became a professor, he spent a few months at the Tata Institute of Fundamental Research, Bombay where he collaborated with K Chandrasekharan in writing the monograph `Typical Means'. (K Chandrasekharan was brought to India in 1949 by Homi Bhabha to build the School of Mathematics in TIFR which he did with great success). Minakshisundaram made a couple of brief visits to the US and in 1958 went to Edinburg to give a half-hour lecture on Hilbert algebras at the International Congress of Mathematicians

Minakshisundaram collaborated with Ake Pleijel, K Chandrasekharan, O Szasz and C T Rajagopal. He also had several research students working with him but unfortunately most of them gave up research after taking their PhD. He tried hard to generate enthusiasm in his students and colleagues for mathematical research. But he found the atmosphere in an Indian University stinging

for creative work. He longed for a place like Princeton where he could work without any hindrance. He was appointed a Professor at the newly created Institute for Advanced Studies in Simla but by then his health was deteriorating after a bad heart attack. He passed away on August 13, 1968

Apart from studying generalised Fourier expansions, Minakshisundaram also proved several interesting results on classical multiple Fourier series. In a joint work with K Chandrasekharan he studied the (Bochner-) Riesz means associated with the double Fourier series. In an earlier work with Otto Szász he studied the absolute convergence of multiple Fourier series

A Fourier series is an **expansion of a periodic function**. **in terms of an infinite sum of sines and cosines**. Fourier series make use of the orthogonality relationships of the sine and cosine functions.

A fitting tribute to Minakshisundaram is enshirined in what is described as **Minakshisundaram coefficient** in Mekean and Singer’s solution of the heat equation, which Minakshisundaram had used. He co-authored a book *Typical Means* (Oxford University Press, 1952).

**Let us remember great Indian Mathematical contributions. **

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