Topic #6 -------------- OP-SF NET 8.3 ---------------- May 15, 2001 ~~~~~~~~~~~~~ From: Martin Muldoon (muldoon@yorku.ca) Subject: Arpad Elbert 1939-2001 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 Academy of Sciences. Through this Institute he received the Academy's degrees of Candidate - equivalent to the North American Ph.D. - (1971) and Doctor of Mathematical Sciences (1989). He had already been awarded the Grunwald Prize for young mathematicians who have already done remarkable work before graduation from 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.

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