## OP-SF WEB

### Extract from OP-SF NET



Topic #6  --------------   OP-SF NET 8.3  ----------------  May 15, 2001
~~~~~~~~~~~~~
From: Martin Muldoon (muldoon@yorku.ca)

Arpad Elbert died in Budapest on April 25th, 2001 after a recurrence of the
illness which had plagued him for nearly a year.  We were heartened by his
apparent recovery after surgery for a brain tumour last summer but,
unfortunately, the recovery was not to last.

Arpad was born in Kaposvar in southwestern Hungary on December 24, 1939 and
graduated in Mathematics from the Eotvos Lorand University, Budapest, in 1963,
being awarded the Medal for Higher Education. The rest of his career was
associated with the Mathematical Institute (founded in 1949 and later
named, after its first Director, the Alfred Renyi Institute) of the Hungarian
Candidate - equivalent to the North American Ph.D.  - (1971) and Doctor of
Mathematical Sciences (1989). He had already been awarded the Grunwald Prize for
the Academy. His most recent position was that of Scientific Advisor, the highest
scientific position in the Institute.

Arpad was the author or co-author of about 100 articles, mostly in the areas of
ordinary differential equations and special functions but including also
contributions to delay differential equations, Fourier analysis, approximation
theory and inequalities. In the great division between theory builders and
problems solvers he belonged the latter group and was always ready to help others
with their mathematical problems. In 1977, John Lewis and I had made the
conjecture that the zeros of the Bessel J_\nu(x) were concave functions of \nu
for \nu > 0.  Soon after, Arpad gave an ingenious proof of the concavity on the
entire interval of definition of the zeros in question. He did this using only
classical tools making especially fruitful use of a formula in G. N. Watson's
"Treatise" on the derivative of a zero with respect to \nu. The formula was
well-known but little used previously.  Later Arpad (mostly with Andrea Laforgia
and occasionally others) was able to make much further use of this and related
formulas in the study of inequalities, monotonicity properties and convexity
properties of zeros of Bessel and related functions.  Whenever I am asked a
question in this or a related area my first reaction is to look at the thirty or
so articles of Elbert and Laforgia.  There is a good summary of some of this work
in the paper based on Elbert's plenary talk at OPSFA-Patras which is to appear in
Journal of Computational and Applied Mathematics.  Arpad's death makes a big hole
in the program for the forthcoming OPSFA Symposium in Rome. I hope that the
time allotted to his lecture can be devoted so some tributes to him and his work.

Arpad was a virtuoso in tough analytic calculations (tools like reversion of
series came to him naturally) with an unerring sense of when an inequality was
sharp and when an approximation might be replaced by an inequality.  In joint
work he alternated this role with that of devil's advocate concerning the
conjectures of others.  This gave a particular added value to a collaboration
with him. As Arpad became better known he had many collaborators and invitations
to visit institutions and conferences in Italy, Canada, Germany, Greece, the
Czech Republic and Japan among other places.  A notable collaboration was that
with Professor T. Kusano (Fukuoka University) on half-linear and other
differential equations.

Arpad will be remembered for his unfailing kindness and courtesy and as a valued
and generaous collaborator.  He is survived by his wife Marika and daughter
Judit, now at the beginning of her own mathematical career. A funeral service
will be held at Felsokrisztinavarosi Plebania Urnatemetoje, Budapest XII. ker.
Apor Vilmos ter 9, at 16:00 on June 29, 2001.

I am indebted to Gabor Halasz for his kindness and promptness in supplying me
with some biographical information and to Lee Lorch for some additional
suggestions.