Professor Eric Russell Love
A note in memorium
The outstanding mathematician Eric Russel Love died on August 7,
2001. Being born on March 31, 1912, Professor Love died peacefully
in his 90th year.
The name of Professor E.R. Love is well known to mathematicians
in such fields of math as fractional calculus, special functions
and integral transforms.
An enormous contribution of Professor Love to the theory of fractional
calculus goes back to his old papers Proc. London Math. Soc., Ser.
2 44 (1938), 1-35 and 363-397. These were his first publications
which made him famous in this field. In the first paper written
together with L.C. Young, a formula of fractional integration by
parts, very useful in fractional analysis, was proved for the first
time, while in the second one the fractional integro-dierentiation
of almost periodic functions was studied.
His next results published in Proc. Edinburgh Math. Soc. (2) 15
(1967), 169-198 and in Proc. Cambridge Philos. Soc. 63 (1967), 1055-1076,
were also pioneer ones in the field of fractional calculus. He was
the first who proved that the composition of two Riemann-Liouville
fractional integrals with power weights yields the generalized fractional
integral containing the Gauss hypergeometric function in the kernel.
Professor Love applied these results to solution of the corresponding
integral equations of the first kind in closed form. Professor Love
also was a pioneer in obtaining suffcient conditions for existence
of ractional integrals of purely imaginary order (J. London. Math.
Soc., Ser.2 (3), (1971), 41-259). His investigation of the so called
index laws for the Riemann-Liouvlille fractional integrals and derivatives
(J. Austral. Math. Soc. 14 ((1972), 385-410 and Fractional Calculus
(Glasgow, 1984), 63-74. Res. Notes in Math.. 138, Pitman, Boston,
MA, 1985) is also well known to specialists.
His other results involving investigation of Lebesgue points of
the Riemann-Liouville fractional integrals (Real Anal. Exchange
12 (1986/87), 327-336), the existence of fractional derivatives
(Real Anal. Exchange 20 (1994/95), 140-157, with B. Ross and S.G.
Samko) and application of fractional calculus to solution of integral
equations Fractional Calculus and its Appl. (New Haven, 1974), pp.
272-288. Lecture Notes in Math., Vol. 457, Springer, Berlin, 1975
and Glasgow Math. J. 23 (1982), 31-40, with T.R. Prabhakar and N.K.
Kashyap) and partial differential equations (Proc. Cambridge Philos.
Soc. 76 (1974), 313-325, with D.L. Clements) and others were also
essential steps in the development of fractional calculus and its
applications.
We also mention the papers by Professor E.R. Love Fractional Calculus
(Glasgow, 1984), pp. 75-86. Res. Notes in Math.. 138, Pitman, Boston,
MA, 1985 and J. Austral. Math. Soc., Ser. B 25 (1983), 161-174,
with B.H.J. McKellar and M.A. Box) devoted to application of fractional
calculus to the inversion of the Struve integral transform and a
series of his papers with A. Byrne J. Austral. Math. Soc. 18 (1974),
325-358, J. London. Math. Soc. (2) (22), (1980), 285-306, Math.
Proc. Cambridge Philos. Soc. 92 (1982), 275-291 and J. Math. Anal.
Appl. 190 (1995), 428-448) where real and complex inversion relations
for the generalized Stieltjes transform were proved.
In a series of papers, Professor Love studied various properties
of special functions (gamma, Bessel, Legendre, etc.), integrals
(singular, oscillatory, Neumann, Ross-Riemann-Stieltjes, etc.),
series (power, Legendre, Fourier-Legendre, etc.) and inequalities
of different type (Hardy, Copson, Cochran, Lee, Knopp, Carleman,
Gabushin, etc.). Investigations there gave an essential contribution
to these fields. One can find the papers in these directions in
the list of Professor Love's publications presented in this volume.
In this list one can also see his publications in other fields,
for example in some problems of functional analysis, potential theory
and even visco-elasticity.
Professor E.R. Love started his work at the University of Melbourne
in 1940. In 1977 he became Professor Emeritus and was appointed
honorary Professional Fellow in Department of Mathematics. In 1991
he was awarded the Honorary Degree of DSc of that university. He
was known to be an excellent teacher. His lectures could be considered
as a model of clarity, accuracy, and completeness not only for students,
but also for all participants of various international conferences,
workshops and seminars. At many of them Professor E.R. Love was
one of the main speakers.
In his activity Professor Love followed the best traditions of
his teachers at the University of Melbourne, from which he graduated
in 1933 with Honours in Mathematics, and at the Cambridge University
where he took his PhD in 1935. He gave a homage to his teachers:
Love's papers devoted to Professor T.M. Cherry (J. Austral. Math.
Soc. 9 (1969), 1-24 and Bull. London Math. Soc. 1 (1969), 224-245)
and to Professor G.H. Hardy (Austral. Math. Soc. Gaz. 25 (1998),
2-5) could produce a big impression on everybody who is interested
in history of science and biography of scientists.
Professor E.R. Love loved people and they loved him. Many people
who knew him, and especially those who had a joint work with him,
felt always an enthusiastic impression he produced on his partners
by his intellect, kindness and respect to others' opinion. The authors
of this note met Professor Love for the first time at International
Conference on Fractional Calculus and Applications (Tokyo, May-June
of 1989) and they were really happy to communicate and collaborate
with him from that time. One of the first impressions was that you
have a pleasure to talk with this man, this impression never disappearing.
Working in math, Professor Eric Russell Love was a man of integrity.
Everybody who met Professor Love always had an impression that they
dealt with a real gentleman and a person living in math, the latter
combination being rather rare. His interest in math was always unfeigned
and keen till his last years. Participants of the Internatinal Conference
on Boundary Value Problems, Special Functions and Fractional Calculus,
devoted to 90th birthday of academician F.D.Gakhov and held in Minsk
in February of 1996, were much impressed both by his comprehensive
talk and his interest to come to the conference from summer time
in Australia to cold winter in Minsk - at the age of almost 85.
It was very surprising that he wore only a suit and summer shoes
without a cap when visiting Minsk Opera and Ballet Theater, while
the temperature in Minsk was minus 15C°.
Professor Eric Russel will be remembered by many people, for his
great contribution to math, genuine manner and enthusiasm.
Anatoly A. Kilbas, Belarusian State University, Minsk, BELARUS
Stefan
G. Samko, University of Algarve, Faro, PORTUGAL
Published in Rev Acad. Canaria Cienc. 11 (1999), No. 1-2, 259-275.
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