Who developed one of the foundations of functional analysis and also taught Hugo Steinhaus?
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Hugo Steinhaus Władysław Hugo Dionizy Steinhaus (January 14, 1887 – February 25, 1972) was a Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the Jan Kazimierz University in Lwów (now Lviv, Ukraine), where he helped establish what later became known as the Lwów School of Mathematics. He is credited with "discovering" mathematician Stefan Banach, with whom he gave a notable contribution to functional analysis through the Banach–Steinhaus theorem. After World War II Steinhaus played an important part in the establishment of the mathematics department at Wrocław University and in the revival of Polish mathematics from the destruction of the war.
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David Hilbert David Hilbert (] ; 23 January 1862 – 14 February 1943) was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.
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Schenkerian analysis Schenkerian analysis is a method of musical analysis of tonal music based on the theories of Heinrich Schenker (1868–1935). The goal is to extract the underlying structure of a tonal movement. The basic tenets of the supporing theory can be viewed as a way of defining the way tonality is articulated. A Schenkerian analysis shows hierarchical relationships among pitches, and draws conclusions about the structure of the passage from this hierarchy. The analysis uses a specialized symbolic form of musical notation that Schenker devised to indicate structural status and "prolongation", by which tones that are not contiguous on the surface can nevertheless be connected, and separated by musical material that arises through elaboration on lower structural levels. A key theoretical concept is that of "tonal space"; The intervals between the notes of the tonic triad form a "tonal space" that is filled with passing and neighbour notes, producing new triads and new tonal spaces, open for further elaborations until the surface of the work (the score) is reached.
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Eduard Stiefel Eduard L. Stiefel (21 April 1909 – 25 November 1978) was a Swiss mathematician. Together with Cornelius Lanczos and Magnus Hestenes, he invented the conjugate gradient method, and gave what is now understood to be a partial construction of the Stiefel–Whitney classes of a real vector bundle, thus co-founding the study of characteristic classes.
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Ralph S. Phillips Ralph Saul Phillips (23 June 1913 – 23 November 1998) was an American mathematician and academic known for his contributions to functional analysis, scattering theory, and servomechanisms. He served as a Professor of mathematics at Stanford University. He made major contributions to acoustical scattering theory in collaboration with Peter Lax, proving remarkable results on local energy decay and the connections between poles of the scattering matrix and the analytic properties of the resolvent. With Lax, he coauthored the widely referred book on scattering theory titled "Scattering Theory for Automorphic Functions". Phillips received the 1997 Leroy P. Steele Prize for Lifetime Achievement.
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Martin Schechter (mathematician) Martin Schechter (born 1930, Philadelphia) is an American mathematician whose work concerns mathematical analysis (specially partial differential equations and functional analysis and their applications to mathematical physics). He is a professor at the University of California, Irvine.
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Julius Ebbinghaus Julius Ebbinghaus (9 November 1885, Berlin – 16 June 1981, Marburg an der Lahn) was a German philosopher, one of the closest followers of Immanuel Kant active in the twentieth century. He was influenced by the Heidelberg school of neo-Kantianism of Wilhelm Windelband, and wrote on philosophy of law and the categorical imperative. Professor at Marburg University (Philipps-Universität Marburg) since 1940; 1954 professor emeritus, continuing lectures until 1966. In October 1945, he became installed as Rector Magnificus by order of the American occupation forces. He was the son of famous psychologist Hermann Ebbinghaus.
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Meyer Jerison Meyer Jerison (November 28, 1922 – March 13, 1995) was an American mathematician known for his work in functional analysis and rings, and especially for collaborating with Leonard Gillman on one of the standard texts in the field: "Rings of Continuous Functions".
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Foundations of mathematics Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics. In this latter sense, the distinction between foundations of mathematics and philosophy of mathematics turns out to be quite vague.
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Continuous functions on a compact Hausdorff space In mathematical analysis, and especially functional analysis, a fundamental role is played by the space of continuous functions on a compact Hausdorff space with values in the real or complex numbers. This space, denoted by "C"("X"), is a vector space with respect to the pointwise addition of functions and scalar multiplication by constants. It is, moreover, a normed space with norm defined by
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Fredholm kernel In mathematics, a Fredholm kernel is a certain type of a kernel on a Banach space, associated with nuclear operators on the Banach space. They are an abstraction of the idea of the Fredholm integral equation and the Fredholm operator, and are one of the objects of study in Fredholm theory. Fredholm kernels are named in honour of Erik Ivar Fredholm. Much of the abstract theory of Fredholm kernels was developed by Alexander Grothendieck and published in 1955.
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Beppo-Levi space In functional analysis, a branch of mathematics, a Beppo Levi space, named after Beppo Levi, is a certain space of generalized functions.
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Steinhaus theorem In the mathematical field of real analysis, the Steinhaus theorem states that the difference set of a set of positive measure contains an open neighbourhood of zero. It was first proved by Hugo Steinhaus.
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Isidore Isaac Hirschman, Jr. Isidore Isaac Hirschman, Jr. (1922–1990) was an American mathematician, and professor at Washington University in St. Louis working on analysis.
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Felix Gantmacher Felix Ruvimovich Gantmacher (Russian: Феликс Рувимович Гантмахер ) (23 February 1908 – 16 May 1964) was a Soviet mathematician, professor at Moscow Institute of Physics and Technology, well known for his contributions in mechanics, linear algebra and Lie group theory. In 1925–1926 he participated in seminar guided by Nikolai Chebotaryov in Odessa and wrote his first research paper in 1926.
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Mathematical formulation of quantum mechanics The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. Such are distinguished from mathematical formalisms for theories developed prior to the early 1900s by the use of abstract mathematical structures, such as infinite-dimensional Hilbert spaces and operators on these spaces. Many of these structures are drawn from functional analysis, a research area within pure mathematics that was influenced in part by the needs of quantum mechanics. In brief, values of physical observables such as energy and momentum were no longer considered as values of functions on phase space, but as eigenvalues; more precisely as spectral values of linear operators in Hilbert space.
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Detlef Laugwitz Detlef Laugwitz (1932–2000) was a German mathematician and historian, who worked in differential geometry, history of mathematics, functional analysis, and non-standard analysis.
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Vitold Shmulyan Vitold Lvovich Shmulyan (Russian: Витольд Львович Шмульян , August 29, 1914 – August 27 1944), was a Soviet mathematician known for his work in functional analysis. The Eberlein–Šmulian theorem is named after him.
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A Course of Modern Analysis "A Course of Modern Analysis: an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions" (colloquially known as "Whittaker and Watson") is a landmark textbook on mathematical analysis written by E. T. Whittaker and G. N. Watson, first published by Cambridge University Press in 1902. (The first edition was Whittaker's alone; it was in later editions with Watson that this book is best known.)
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Studia Mathematica Studia Mathematica is a Polish mathematics journal published since 1929. It was founded by Stefan Banach and Hugo Steinhaus. It accepts papers written in English, French, German, or Russian, primarily in functional analysis and related areas such as probability theory.
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Augustin-Louis Cauchy Baron Augustin-Louis Cauchy FRS FRSE (] ; 21 August 1789 – 23 May 1857) was a French mathematician and physicist who made pioneering contributions to analysis. He was one of the first to state and prove theorems of calculus rigorously, rejecting the heuristic principle of the generality of algebra of earlier authors. He almost singlehandedly founded complex analysis and the study of permutation groups in abstract algebra. A profound mathematician, Cauchy had a great influence over his contemporaries and successors. His writings range widely in mathematics and mathematical physics.
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Jacques Hadamard Jacques Salomon Hadamard ForMemRS (] ; 8 December 1865 – 17 October 1963) was a French mathematician who made major contributions in number theory, complex function theory, differential geometry and partial differential equations.