Opening Words

Kristian Seip

Korenblum Fiesta, Barcelona
November 20 - 22, 2003

Dear Boris and dear friends of Boris's! On behalf of the organizers, I am happy to welcome you all here, for this celebration of Boris's 80th birthday and his contribution to our science. I think Barcelona is close to perfect for what we want this meeting to be, a rather informal gathering of close scientific and personal friends of Boris in a relaxed atmosphere, with excellent food, wine, and pleasant surroundings. I know that you, Boris, as many of us do, have enjoyable memories from time spent here, and this certainly makes Barcelona not less appropriate as the place for this meeting. So I am very happy that Joaquim took to the job of organizing the meeting, and since I did very little myself, I dare say he has taken care of it in an excellent way.

I will not give complete review of Boris's scientific life -- we will learn more about that during the meeting. But I will mention two highlights. I believe the first may come as a surprise to you. It is from CT -- computed tomography. I quote from the introductory chapter entitled “In the Beginning” by Steve Webb from the 1988 The Physics of Medical Imaging: “It is perhaps less known that a CT (Computed Tomography) scanner was built in Russia in 1958. Korenblyum et al (1958) [Tetel'baum, Tyutin] published the mathematics of reconstruction from projections together with experimental data and wrote: ‘At the present time in Kiev Polytechnic Institute, we are constructing the first experimental apparatus for getting X-ray images of thin sections by the scheme described in this article’” May I remind you about the fact that G. N. Hounsfield received the 1979 Nobel Prize for Physiology and Medicine for his construction of a machine used to X-ray computed tomography in a clinical environment. I suspect that a neutral observer may find that Boris's achievements in this field are more significant than our precious theory of Bergman spaces. Let me add that Boris has kept his interest for Physics. As late as last year he published a paper entitled "Classical Properties of Low-Dimensional Conductors: Giant Capacitance and Non-Ohmic Potential Drop", with Emmanuel Rashba, in Physics Review Letters!

Let me make a big jump to something we all know well -- the two famous Acta papers. There are probably not many people who have really penetrated all aspects of those papers. The reviewer, Walter Hayman, ended his review of the first in Math Reviews with the following words: “The above sketch must suffice to give some idea of this extremely complicated but profound paper.” I have personally been very much inspired by those papers, which contain amazing and deep ideas. One of the most striking aspects is the way linear programming enters the study of zero sets for analytic functions. I am not able to guess how you got the necessary insight, but it is clear that it is based on a broad knowledge and understanding. As far as I know, there is no other way of getting such precise estimates for zero sequences for functions in Bergman spaces.

Boris played a decisive role in the development of the theory of Bergman spaces since around 1990, both through his papers and as a mentor. I asked Håkan about Boris's role as a mentor, and got the following words from him: “I think Boris is one of the truly passionate mathematicians. He really believes that Mathematics is important to the real world, and is willing to discuss it at length at any time, not just during working hours. He gave a lot of support at a time when I felt my mathematical ideas met with little or no response, and I was not sure that I wanted to continue doing mathematics. He also gave me a whole new (to me) field to study: the Bergman space(s). The maximum principle he was then working on suggested that really new phenomena could appear here. I got the idea to introduce extremal problems, in a very simple setting with a single zero at first; the buzz-word we used in these early discussions with Boris was the ‘envelope’. Boris was always very generous, and refused co-authorship when he felt that his contribution was not quite up to the mark he set. The work on the ‘envelope’ gave rise to the factorization theory you now know. The use of Green's formula and the like was stimulated by a paper of Boris, ‘Transformation of zero sets by contractive operators in the Bergman space’, which should be appreciated better than at present.”

The last statement is certainly interesting; I believe Håkan is right. There are probably ideas in that paper that should be pursued and that could give more insight into the zero sets of Bergman spaces. I know Boris himself has thought and still thinks about that.

Mathematics has obviously meant a lot to you, Boris, but we know there have been hardships in your life of a different caliber than most of us have experienced, such as your service as a soldier in the Red Army during World War II and your painful procedure for emigration as well as immigration to Israel and the US. Most of us know little about these sides of your life. What we know is your passion for mathematics, your generosity with ideas and willingness to help fellow mathematicians. I asked another friend of mine about Boris, and got the following response: “Boris always works independently of others. He uses to find new questions that are of interest to him regardless of whether they are fashionable or not. Yet pretty often those questions happen to be the key ones in new areas.” The theory of Bergman spaces certainly is a good example in this respect!

Let's move on with Science. I wish you all an interesting and pleasant time in Barcelona, and to you Boris, I also say: Happy Birthday!