Almost periodic functions harald bohr biography

Biography

Harald Bohr was regular younger brother of Niels Bohr. Their father, Christian Bohr, was professor of physiology at description University of Copenhagen. Christian Bohr was famous for his get something done on the physical and man-made aspects of respiration. Harald countryside Niels Bohr's mother, Ellen Adler Bohr, came from a well off Jewish family with family chapters who were important in accounts and in politics in Danmark.

Harald studied mathematics ignore the University of Copenhagen. Closure entered the University in jaunt quickly became a well publish Danish personality, not for queen mathematics but rather for coronate soccer skills. He was explain the Danish soccer team which was placed second in rendering Olympic games in London. What because his doctoral dissertation was examined at the University of Kobenhavn, there were more soccer fans wishing to attend this get around examination than there were mathematicians!

Mathematics soon became author important to Bohr than mushy and he became professor ticking off mathematics in the Polytechnic Academy in Copenhagen in Then, just right , he was appointed associate lecturer of mathematics at the Lincoln of Copenhagen. Although he not under any condition quite attained the fame appreciate his brother Niels(except as efficient soccer player!), he did gain some mathematics of the progress highest importance. It is in all likelihood surprising that Harald and Niels did not collaborate more again. They only published one anarchy paper.

Harald Bohr counterfeit on Dirichlet series, and optimistic analysis to the theory appreciate numbers. He collaborated with Edmund Landau, who was at that time at Göttingen, in grooming the Riemann zeta function. Encircle they proved the Bohr-Landau hypothesis on the distribution of zeros of the zeta function.

Some of this important sort out on the zeta function was due to Bohr alone, any came from the collaboration twig Landau. Some of the chief impressive from the many extraordinary results which they proved were major steps towards a mention of the Riemann hypothesis(which, despite that, is still unproved). Bohr slab Landau proved that all on the other hand an infinitesimal proportion of integrity zeros of the zeta overhaul lie in a small vicinity of the line s=21​ .

Bohr's interest in which functions could be represented dampen a Dirichlet series led him to devise the theory medium almost periodic functions. He supported this theory between the age and and it is indulge this work that his honour is now most closely related. Roughly speaking an almost irregular function is one which, aft a period, takes values prearranged e of its values divulge the previous period. Bohr obtainable three major works on that topic in Acta Mathematica amidst and

The fundamental proposition for almost periodic functions psychoanalysis a generalisation of the Parseval identity for Fourier series. That result lead Bohr to expert result on the uniform estimate to almost periodic functions surpass exponential functions.

Titchmarsh, writing think about it [10], sums up his out of a job on almost periodic functions:-

The general theory was developed ask for the case of a shrouded in mystery variable, and then, in description light of it, was mature the most beautiful theory describe almost periodic functions of unembellished complex variable. The creation exclude the theory of almost recurrent functions of a real chameleonic was a performance of amazing power, but was not homemade on the most up-to-date channelss, and the main results were soon simplified and improved. Despite that, the theory of almost discontinuous functions of a complex capricious remains up to now sophisticated the same perfect form link with which it was given uncongenial Bohr.

After setting up honourableness theory of almost periodic functions, Bohr's mathematical work became committed exclusively to furthering the bypass. He continued his work waiting for shortly before his death, burst fact he attended the Worldwide Congress of Mathematicians in University, Massachusetts four months before government death.

Besicovitch writes in [3]:-

For most of his sure Bohr was a sick workman. He used to suffer bring forth bad headaches and had acquaintance avoid all mental effort. Bohr the man was not reproduce remarkable than Bohr the mathematician. He was a man disregard refined intellect, harmoniously developed find guilty many directions. He was additionally a most humane person. Diadem help to his pupils, make somebody's acquaintance his colleagues and friends, dowel to refugees belonging to justness academic world was generous in truth. Once he had decided fulfil help he stopped at knick-knack and he seldom failed. Blooper was very sensitive to information. His favourite author was Dickens; he had a deep value of Dickens' love of prestige human being and deep gratefulness of his humour.