Biographical Memoirs Volume 63 (1994) / Chapter Skim
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9. Einar Hille
9. Einar Hille
Pages 218-245
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From page 219... ...
He was president of the American Mathematical Society (1947-48) , and a member of the National Academy of Sciences, the Royal Academy of Sciences of Stockholm, and the American Academy of Arts and Sciences.
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But from the ninth grade on mathematics was one of my best subjects ant! ~ ctict outside reacting in this subject regularly from the tenth gracle on." Hille entered the University of Stockholm in the fall of 191~ with the aim of becoming a secondary school teacher.
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He spent 1919-20 doing office work in the Swedish Civil Service anti teaching on the sicle at the University of Stockholm. His big break came in 1920 when a fellowship from the Sweclish-American Foundation enabled him to spend the year at Harvard University; this was follower!
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A touching account of this collaboration can be found in Hille's "In Retrospect." 2 Hille and Tamarkin started with the problem of the frequency of the characteristic values of linear integral equations (192S, 3; 1931, I) and continued on to study other phases of integral equations (1930, 2; 1934, 41.
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Curtz, ~ 960; and Sister Mary Zachary Brunell, 1964. Up to this point in this chronicle my main source has been Hille's own account of his early years published in the essay, "In Retrospect"3 anct preprints entitled "Home, Schools, Avocations" and "Accomplishments." Material for the previous paragraph was taken from ~acobson's article entitled "Einar Hille, His Yale Years, A Personal Recollection."4 In what follows ~ have relied on my forward to Hille's selected papers5 and Yosicia's article, "Some Aspects of E
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From page 224... ...
This chapter contains a basic generation theorem, giving necessary anc! sufficient conditions for an operator to generate a semi-group holomorphic in a sector, as well as a characterization of the convex hull of the spectrum of the infinitesimal generator in terms of the exponential growth of the semi-group of operators along the various rays in the sector of definition.
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From page 225... ...
In August of 1944 Hille delivered the colloquium lectures at the American Mathematical Society meeting and immediately thereafter he started in earnest writing his book,8 Functional Analysis and Semi-Groups, which was finally published in 1948. Tt was both a textbook on functional analysis and a monograph on the theory of semi-groups of operators.
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The spectral theory chapter is outstanding. It is based on an operational calculus explicitly constructed for the generators of semi-groups of operators.
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The chapters on trigonometric semi-groups and translation semigroups are related to factor sequences for Fourier series and factor functions for hip spaces, which Hille dealt with in earlier papers (~1924, I; 1926, 4; 1933, I, 511. The chapter on partial differential equations is somewhat ctisappointing in that it did not anticipate the most successful approach to the subject via the Hille-Yosida theorem.
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The theory of commutative Banach algebras is introduced early in the book and plays a major role in the chapters on spectral theory en cl holomorphic semi-groups. The influence of Yosicia and, to some extent, Feller is quite evident; and of course ~ took advantage of my being coauthor by including my own results on extencled classes of semi-groups (ctistinguished by their behavior at the origin)
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. He showed that the ACP has at most one solution of normal type if Uis a closed operator whose point spectrum is not ciense in the right halfplane.
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; see also (1956, 21. He had given himself the problem of finding necessary and sufficient conditions on the coefficients a and b that the maximally defined operators ~ and C (i.e., with no boundary conditions)
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wit) belong to a complex noncommutative Banach algebra B with unit fizz being analytic in z.
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, he calculated the transfinite diameters of the unit spheres of some complex Banach spaces. After retiring from Yale in 1962, Hille stayed in New Haven for two more years and then started on a nomadic existence that took him from one visiting teaching post to another for the next eight years before encling up at the University of California at San Diego.
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N Jacobson, Einar Hille, His Yale Years, A Personal Recollection: Integral Equations and Operator Theory, Vol.
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26:241-48. On the zeros of the functions defined by linear differential equations of the second order.
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On the characteristic values of linear integral equations.
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On the characteristic values of linear integral equations.
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1934 .. Uber die Nullstellen der Hermiteschen Polynome.
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47:80-94. A class of differential operators of infinite order.
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XXXI. New York: American Mathematical Society.
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1:22736. Quelques remarques ser les equations de Kohnogoroff.
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Sci. Remarks on differential equations in Banach algebras, studies in mathematical analysis and related topics.
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Functional analysis.
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20:20-32. Quatre Lecons sur des Chapitres Choicis d'Analyse.
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- 1981 With Frank Cannonito. An elementary proof of the Jordan normal form theorem based on the resolvent.
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