**Werner Rogosinski**was known to his friends and colleagues as

**Rogo**. His parents were Hermann Rogosinski, a counsellor in Breslau, and Helma Braun. Werner was born in Breslau, at that time a German town, although his parents were from Jewish Polish families. The city is now in Poland and known by its Polish name of Wrocław. Werner had a sister Lotte and a younger brother Kurt. It was a musical family and Werner learnt to play the piano and violin as a child. His brother Kurt became a professional pianist.

In 1900, Werner entered the St Maria Magdalena Gymnasium in Breslau [2]:-

Rogosinski graduated from the Gymnasium in 1913 and entered Breslau University to study mathematics. However, World War I began in July 1914 and, in the following month, Germany declared war on both Russia and France. Rogosinski's studies were interrupted by the war and he undertook military service as a corporal in the medical corps. When he was able to continue his studies he spent time at Freiburg im Breisgau before moving to Göttingen to study for his doctorate. At this time Göttingen University was probably the best place in the world to study mathematics and Rogosinski flourished, undertaking research directed by Edmund Landau. At this stage Landau was interested in number theory, in particular Dirichlet series that he had studied for his own doctorate, and it was in this area that Rogosinski worked for his thesis. The particular problem Rogosinski studied involved the Dirichlet divisor problem, particularly studying a series expansion given by Georgy Voronoy. Now Landau had managed to get some new results but had failed to solve other variants. Rogosinski gave a new proof of Voronoy's results as well as solving the cases which had baffled Landau [2]:-This was a humanistic gymnasium with strong emphasis on Latin and Greek at which Werner excelled. There was little science and the mathematics course contained no calculus but plenty of geometry. Rogo was happy at school and considered that the training obtained there provided an excellent background for a future pure mathematician. He remained all his life strongly opposed to early specialisation.

This work appeared in Rogosinski's doctoral dissertationRogosinski's solution greatly pleased Landau and it was from this time that their close friendship developed.

*Neue Anwendung der Pfeifferschen Methode bei Dirichlets Teilerproblem*which he submitted to Göttingen University in 1921 and was awarded the degree on 25 January 1922. Landau was an outstanding mathematician but he had a reputation as having an arrogant manner which annoyed his colleagues. He was held in awe by the many bright young students he supervised, but Rogosinski seems to have had a rather different relationship with him. This is illustrated by a nice little episode related by Walter Hayman [2]:-

Rogosinski was appointed to the University of Königsberg as a Privatdocent in 1923 and began publishing papers which typified the contributions he made throughout his life to the theory of functions and to the theory of series. In the following years he publishedOn one occasion[Rogosinski]cut out photographs of the heads of all[Landau's graduate students]and assembled them as a picture of a group in a little perambulator being pushed by Landau dressed as a nurse from Spreewald. Landau, to whom the picture was presented, placed it where everyone was bound to see it sooner or later!

*Über Bildschranken bei Potenzreihen und ihren Abschnitten*(1923),

*Zur Theorie der Dirichletschen Reihen*(1924),

*Ein Satz tiber Dirichletsche Reihen*(1924),

*Über die Abschnitte der Fourierreihen*(1924), and

*Über die Abschnitte trigonometrischer Reihen*(1925). When Rogosinski arrived at the University of Königsberg, the Mathematics Department was small but had an excellent ordinary professor in Konrad Knopp. In 1925 Richard Brauer arrived but the arrival of Gábor Szegő in 1926 was particularly important to Rogosinski since the two quickly became both firm friends and mathematical collaborators. Their first joint paper was

*Über die Abschnitte von Potenzreihen, die in einem Kreise beschränkt bleiben*(1928). The Department was further strengthened in 1927 with the arrival of Kurt Reidemeister.

Erna Raphael, a friend of Rogosinski's sister Lotte from a young age, had been a friend from childhood. Werner and Erna wanted to marry but had to wait until he was earning a salary, rather than living in relative poverty which was the position of a Privatdocent. This happened in 1928 when he was promoted to an extraordinary professor and, on the 27 September of that year, Werner and Erna were married. The next five years were excellent ones for the Rogosinskis. A steady stream of high quality papers was supplemented in 1930 by the publication of his first book, namely *Fouriersche Reihen* . This book on Fourier series was based on lectures that Rogosinski gave on the topic at the University of Königsberg. His students had not studied the Lebesgue integral so the book did not use this approach, something that Rogosinski planned to change in a new edition but political events in Germany over the following few years meant that all plans had to be cast aside. Before we look at these events, however, we note the hospitality that the Rogosinskis' home in Königsberg offered to their wide range of friends. The family increased in size in 1932 with the birth of their son Peter.

Life changed for all German people of Jewish background in 1933 when Hitler came to power. On 1 April there was the so-called "boycott day" when Jewish shops were boycotted and Jewish lecturers were not allowed to enter the university. On 7 April 1933 the "Restoration of the Civil Service" Law was passed which provided the means of removing Jewish teachers from the universities and, of course, also to remove those of Jewish descent from other roles. All civil servants who were not of Aryan descent (having one grandparent of the Jewish religion made someone non-Aryan) were to be retired. There was, however, a clause which exempted those who had fought for Germany in World War I or had been in office since August 1914. Reidemeister was forced to leave his chair in Königsberg in 1933 by the Nazis, who he strongly opposed, since they classed him as 'politically unsound'. Richard Brauer, being Jewish, was dismissed from his Königsberg position. Both Szegő and Rogosinski had fought for Germany in World War I so were not immediately dismissed. Despite the terrible position that Rogosinski was in his fine sense of humour did not desert him [2]:-

Szegő gave up the struggle against the Nazi anti-Semitic policies and, anticipating his dismissal, accepted a position at Washington University at St Louis in 1935. Rogosinski carried on despite his position becoming more and more difficult until, in 1936, he was dismissed from his professorship. He moved to Berlin and, during the year 1936-37, taught mathematics in Jewish schools there. His life was saved in 1937 by G H Hardy and J E Littlewood when, realising the danger he was in and also the remarkable mathematics he had produced, they invited him to England to join them at the University of Cambridge. Rogosinski went immediately to Cambridge and, six months later, his wife and young son Peter joined him. There followed a few difficult years having to live on a small grant which had been provided by the Society for the Protection of Science and Learning following strong recommendations from Hardy and Littlewood. However, collaboration between these fine mathematicians provided Rogosinski with a period of exceptional productivity and enjoyment. In 1939 his important paperIn1934he told his colleagues that if the Nazis revoked his Venia Legendi he would open a cigar shop near the university and supply his former colleagues and the administrative personnel with cigars having special labels.

*On subordinate functions*appeared in the

*Proceedings*of the Cambridge Philosophical Society, communicated by G H Hardy. Rogosinski begins the paper as follows:-

In 1941 the University of Aberdeen, having a number of staff on war service, appointed Rogosinski as an assistant lecturer in mathematics. The pay was poor and the position was far too junior for a fine mathematician like Rogosinski at the peak of his abilities but it provided him with a stepping stone which must have made him feel that he was fortunate. He also found a colleague in A J Macintyre (married to the mathematician Sheila Macintyre) who joined him in an interesting collaboration. Together they published the noteThe so-called Lindelöf principle is nothing more than a transformation and systematic application of the simple Schwarz lemma. Nevertheless, it is a very powerful tool for the solution of many questions in the theory of functions. It is based on the conception of "subordinate" functions. In this paper I make some further observations on this principle and also aim at giving precision to it in the case of "locally schlicht" functions.

*Some elementary inequalities in function theory*(1945) and later the major 50-page paper

*Extremum problems in the theory of analytic functions*(1950). In 1944 Rogosinski's collaboration with Hardy led to the publication of their book

*Fourier Series*. This was, in many ways, the book that Rogosinski had planned as a rewrite of

*Fouriersche Reihen*but based on the Lebesgue integral. E C Titchmarsh writes [5]:-

A second edition of this work was published in 1950, a Russian translation was published in 1959 (reprinted in 1962), and a Czech translation was published in 1971.... the appearance of a Cambridge tract by Hardy and Rogosinski is to be welcomed. It is definitely a book for the pure mathematician, but it should appeal to a large class of readers. It is really quite easy to read. A fair background of knowledge is an advantage, though very little is assumed. The theory is introduced in a "modern" manner; "Hilbert space", "strong convergence", "closure", "completeness", and general methods of summability are the conspicuous features. ... We believe that it will give a great many mathematicians all over the world as much pleasure to read, as it must have given the authors pleasure to write.

Rogosinski lectured to the Edinburgh Mathematical Society in the summer of 1945 and, a consequence of this lecture became the book *Volume and integral* (1952) published in the Oliver and Boyd Series of University Mathematical Texts. Winifred Sargent begins her review of this undergraduate text as follows [4]:-

Reviewing the same book, Ralph Jeffery writes:-This new and welcome addition to a well known collection provides a clear and, in view of its price and size, a surprisingly comprehensive introduction to the theories of measure and integration in Euclidean spaceR_{n}of n dimensions.

In 1945 Rogosinski moved to Newcastle when he was appointed as a lecturer at King's College, University of Durham (King's College did not become the University of Newcastle until 1963). There he was promoted to reader in mathematical analysis in 1947 and then to the chair of pure mathematics at King's College in 1948 when A C Offord resigned to take up his appointment to the chair at Birkbeck College, London. He also became head of the Mathematics Department and Walter Hayman writes of his time in this role in [2]:-This book has been written "primarily for third year Honours students" in the Universities of Great Britain. ... This book is well suited for the purpose the author had in mind. It gives a complete treatment of absolutely convergent integrals in Euclidean space. The proofs are brief and elegant, and at the same time easy to follow.

In November 1953, J E Littlewood proposed Rogosinski for admission into the Royal Society of London. The proposal was seconded by A S Besicovitch, J C Burkill, A E Ingham, M L Cartwright and W D V Hodge. They describe his qualifications in a rather understated way as follows:-He was an excellent Head of Department with a real flair in his appointments. Nearly all of the men he first chose have become professors or readers. ... in Newcastle[the Rogosinskis' hospitality]flourished as never before. After every Colloquium all the staff in pure mathematics were invited in, perhaps15persons in all and the tables were covered with delicious food. Werner was himself a most stimulating lecturer, convinced of the tremendous importance of mathematics and taking a great delight in every new result that was proved. In all this he was most generous. On one occasion he produced a fine theorem. When he told one of his younger colleagues about this, the latter suggested a slight generalization. Rogo was very pleased and refused to remember in any way that he had made the original discovery.

Rogosinski was elected a fellow of the Royal Society on 18 March 1954. Another similar distinction which was given to him was election to the Danish Academy of Sciences in 1962. In fact, after retiring from the King's College chair in 1959, he had moved to Denmark where he had been invited to join the Institute of Mathematics at Aarhus. He spent the last years of his life there.Distinguished for his contributions to Mathematical Analysis, especially in the theory of Fourier Series and Allied Subjects.

Walter Hayman paints a nice picture in [2]:-

Rogosinski was a good and kind man genuinely loved by all who knew him. His cheerfulness and vitality were enough to infect any company he was in and where he was it was truly 'gemtitlich'. Beneath his cheerful and out-going nature he had however a serious side. Thus he felt deeply about the events that had happened in Germany and would never go back there. Although in very poor circumstances himself he helped his sister and her husband to escape. His mother and elder brother Rudolf were less fortunate. Mention has been made of Rogo's interest in music. He hated anyone to cough or make a noise let alone talk when music was being played in the Concert Hall or in the home. He also collected stamps, English Commonwealth and old German. He liked going for long tramps. Mathematics was his passion and in his company it was impossible not to believe in the importance of mathematics generally and classical analysis in particular.

**Article by:** *J J O'Connor* and *E F Robertson*