# George Olatokunbo Okikiolu

### Quick Info

Aba, Nigeria

**George Okikiolu**is a Nigerian mathematician and inventor who published papers on integral operators on Banach spaces.

### Biography

**George Olatokunbo Okikiolu**was the son of James Adekunle Okikiolu (1907-1998) and Anwan Obong (1911-1970). James Okikiolu was a Yoruba from Abeokuta in Western Nigeria while Anwan was a daughter of the Obong of Calabar, a title which essentially means the King of Calabar. James was a medical doctor and he met Anwan, who had trained as a nurse, while both of them were working in a hospital in Abeokuta in Western Nigeria. At this time Nigeria was a British colony and most of the doctors and other staff in the hospital were British. George had a twin sister Elizabeth O Okikiolu. Their parents gave their children the names George and Elizabeth after the recently crowned king and queen of Great Britain.

Okikiolu explained about his early education and upbringing in [1]:-

After early primary schooling in Lagos and at Ibadan, my secondary schooling was at Baptist Boys' High School in Abeokuta, where I lived during term times. I was often away from school to recuperate at home from feverish complaints, but I made sure my performance at school was not below my usual best. Although my childhood experiences in and around hospitals made me feel that I would like to grow up to be a medical doctor, my interests in mathematics and the physical sciences had developed, and I pursued those subjects at university ...In 1959 George, his twin sister Elizabeth, and a younger brother Victor O Okikiolu (born 6 May 1944) sailed from Lagos to England on the ship

*Aureol*. After calling at Takoradi and Freetown, they arrived in Liverpool, England, on 13 July 1959. They all give the address at which they will first reside as 24 Thornton Lodge Road, Huddersfield, Yorkshire. George and his twin sister Elizabeth took accommodation at 29 Ravenshaw Street, Hampstead, London, and George Okikiolu matriculated at Sir John Cass College on Jewry Street. This College, which has an interesting history, had been the Sir John Cass Technical Institute from 1902 to 1950 when it changed its name to the Sir John Cass College in recognition of its broadening provision of courses. The College could not award degrees but it delivered courses which were aimed at students taking the University of London examinations to qualify for a University of London external degree. The college is now part of the Metropolitan University of London.

While studying mathematics at the Sir John Cass College, Okikiolu met a fellow student, an English girl Patricia Natasha Edwards [2]:-

... from a family with a trade-union background and a central interest in class struggle.George and Patricia Okikiolu were married on 19 September 1962. After the marriage Okikiolu, his wife, and his sister, all lived at 29 Ravenshaw Street, Hampstead. In 1963 Okikiolu graduated with a B.Sc. degree with First Class Honours in Mathematics, from the University of London. Later that same year, on 30 December, he submitted his first paper for publication to the London Mathematical Society. The paper,

*A generalisation of the Hilbert transform*, was published in the Journal of the London Mathematical Society in 1965. His address on the paper is Department of Mathematics, Sir John Cass College, Jewry Street, London.

After the award of his first degree, in 1964 Okikiolu accepted an assistant lectureship at Battersea College, London, while continuing to study for a Master's Degree from the University of London. In his Master's thesis on real and complex variable analysis, he looked in particular at lower densities in measure theory. He was awarded an M.Sc. in 1964. While on the one-year appointment at Battersea College, Okikiolu applied for assistant lectureships in various universities and was offered an appointment at the University of Sussex. He began teaching there in the autumn of 1965. His second daughter was born shortly before he took up the appointment at the University of Sussex so let us comment briefly about his two children. We note that by 1965 only Elizabeth Okikiolu is at 29 Ravenshaw Street, Hampstead, while George and Patricia Okikiolu were living at 11 Beverley Gardens, Richmond upon Thames, England.

George and Patricia Okikiolu's first child was Jeannie Adetokunbo Okikiolu. She was awarded an MA from the University of Cambridge where she studied mathematics. She trained as a chartered accountant before working as a forensic accountant. Their second daughter, Katherine Adebola Okikiolu (born 1965), known at Kate Okikiolu, became a mathematician and has a biography in this archive.

After one year at the University of Sussex, Okikiolu was offered an appointment at the University of East Anglia in Norwich, Suffolk, which he took up in 1966. Okikiolu did not write a Ph.D. thesis but published extensively in the leading mathematical journals. His paper

*On integral operators associated with the Hilbert transform*, where he gives the address Mathematics Division, The University of Sussex, Brighton (England), was submitted for publication 17 March 1965 and published later that year. On 24 June 1965 he submitted the paper

*Fourier transforms and the operator*H_{±}. It appeared in 1966 with the following abstract:-

This is one of a number of papers in which the author studies the properties of the transform H_{±}(f) and allied operators. In this case, identities involving these operators and the Fourier transform are obtained, and these are applied in giving alternative proofs to certain inversion processes derived by the author elsewhere.Indeed it was one of "a number of papers", being one of the nine papers that Okikiolu published in 1966. One of these papers,

*Bounded linear transformations in Lp -space*, was submitted to the London Mathematical Society on 19 October 1964 and was published in the Journal of the London Mathematical Society in 1966. It has two addresses, Mathematics Division, The University of Sussex, Falmer, Brighton, and University of East Anglia, Norwich.

Kate Okikiolu writes [2]:-

My father ... went on to a position in the mathematics department of the University of East Anglia. While I was growing up, the elementary school I attended was extremely ethnically homogeneous. I was unable to escape from heavy issues concerning race, which my mother always explained in a political context.By 1970 Okikiolu had published 24 papers and was writing the book

*Aspects of the Theory of Bounded Integral Operators in Lp Spaces*, which was published by

*Academic Press*in 1971. The Preface to the book begins as follows:-

In this text I have endeavoured to present a fairly detailed account of some of the techniques usually employed in the study of integral operators in Lp -spaces. The methods apply to various special operators, some of which are treated in detail. Although most of the book is concerned with Lp -spaces and operators in Lp -spaces, I have introduced, in the first chapter, some of the basic results in normed linear spaces which apply in particular to Lp -spaces. The second chapter contains a treatment of measures on measure spaces and the Lebesgue integral. These chapters, which are introductory, may be omitted by the reader who is familiar with the general theory; they have been included to make the book to a large extent self-contained, and will be found suitable for undergraduate students studying analysis in their last year at university. The chapters also provide an introduction for the graduate student in the subjects treated.Okikiolu took his 24 papers and this book and submitted them to the University of London for a D.Sc. which he was awarded in 1971. In 1972 he set up the Okikiolu Science and Industrial Organisation, London, and began to create inventions and apply for patents for them. By 1974, unhappy that he was not being promoted to a professorship despite having published around 30 papers in the ten years 1965-74, he decided to resign his university appointment and concentrate on his inventions. In fact his paper

The other chapters of the book are arranged as follows:

Chapter 3 deals with most of the result involving Lp -spaces which will be applied in considering operators. This chapter, which is a sequel to Chapter 2, contains some of the basic results used in the proofs of conclusions in subsequent chapters.

In Chapter 4, the general inequalities which justify the boundedness of some integral operators in Lp -spaces are considered. These include some results which have previously not appeared in books, as do some later chapters. The inequality of Young for convolutions of functions defined on Euclidean spaces is derived as a special case of a general inequality from which other well-known results may also be obtained. Also included here are the inequalities for homogeneous kernels; extensions of the well-known inequality of Schur, which have proved useful for treating fractional integrals and allied transforms. Among the general theorems are results involving convolution operators which approximate to the identity. Various identities and inversion processes are also included.

The results of Chapter 5 are concerned mainly with the theory of interpolation of bounded operators between Lp -spaces, and the theory of rearrangements of functions. Having treated the Riesz-Thorin convexity theorem and one of its extensions, the Marcinkiewicz-Zygmund interpolation theorem is considered after a preliminary treatment of distribution functions. Most of the detailed analysis involving the non-increasing rearrangements of functions is considered in this chapter ...

*Uniformly bounded projections and semi-groups of operators*, published in 1974, gives his address as Okikiolu Science and Industrial Organisation, 23 Mile End Road, Norwich. Since we mention this paper, let us give its Abstract:-

Classes of operators called uniformly bounded projections defined on Banach spaces have been formally introduced, and their connexions with semi-groups of operators considered. Notable cases of such operators include the Dirichlet integrals which are connected with the semi-group of Poisson operators in Lp . In the main conclusions of this paper, there is an exposition of the connexion between classes of uniformly bounded projections and semi-groups of operators. In particular, it is shown that certain uniformly bounded analytic semi-groups of operators give rise to classes of uniformly bounded projections. Various of the known special cases in Lp are also considered as Fourier transform multiplier operators with characteristic functions of intervals as multipliers.His daughter Kate Okikiolu writes [2]:-

My parents separated after my father resigned his university position to focus on his inventions, and my mother then finished her education and became a school mathematics teacher. We moved to a very cosmopolitan area of London, which was like a new birth for me; it was there that my interest in mathematics really began.Okikiolu and his wife separated in 1974 and were formally divorced in 1980.

In [1] Okikiolu writes about his inventions:-

My initial inventions included a proton extractor, electro-chemical oscillator, and magnetic-wave generator, but they were not very promising for commercial development, so I considered other new ideas. Two of my main inventive projects include photoconverter technology and television cameras for infrared and other wave forms. Television cameras for various wave forms relate especially to some of my inventions which operate as remote effect devices involving systems for generating pressure waves affecting human subjects. Other notable inventions include polarvisible inscriptions, which are visible only to viewers equipped with suitable polarizer elements; linear and rotary motor assemblies; light-operated photocell-inductor motors for operating electrical generators; hydraulic projections of electrical terminals for various electrical effects; various forms of television assemblies; composite motor-generators for electrical equipment and electrical vehicles; and nuclear fusion systems. By 1975, I had accumulated and published twenty-five United Kingdom patent specifications. As with some forms of industrial developments, productions relating to my inventive projects have been limited by financial considerations.Despite this work on inventions, Okikiolu continued to published many mathematical papers and books. His two volume work,

*Special integral operators*, was published in 1980, 1981 by his own Okikiolu Science and Industrial Organisation. The two volumes, of around 300 and 500 pages respectively, are subtitled

*Weierstrass operators and related integrals*and

*Poisson operators, conjugate operators, and related integrals*. He had published a small book in 1976, namely

*Completion of the Magic Square of Even Order*, again published by his own Organisation.

In 1981 Okikiolu began publishing a mathematical journal with the title

*Bulletin of Mathematics*. By 1986 twenty-one parts had been published each part containing 2, 3 or 4 papers by Okikiolu. The journal stopped publication in 1986 and by that time Okikiolu had published around 60 papers in it. Only one paper by a mathematician other than Okikiolu appears to have been published in this journal. In 1989 he published another book, namely

*Divisibility and Numbers*. In [1] he writes:-

In 1990, I commenced publication of my books ...but we have been unable to find any books published by Okikiolu after 1989.

### References (show)

- M Cook, George Olatokunbo Okikiolu,
*Mathematicians. An Outer View of the Inner World*(Princeton University Press, 2009). 96-97. - M Cook, Katherine Adebola Okikiolu,
*Mathematicians. An Outer View of the Inner World*(Princeton University Press, 2009). 98-99. - George Olatokunbo Okikiolu,
*Dawn Commission*. http://dawncommission.org/akinkanjuDetail.php?id=70

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Written by J J O'Connor and E F Robertson

Last Update May 2019

Last Update May 2019