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Errett Bishop
Errett Albert Bishop (July 14, 1928 – April 14, 1983) was an Americans, American mathematician known for his work on analysis. He expanded constructive analysis in his 1967 ''Foundations of Constructive Analysis'', where he Mathematical proof, proved most of the important theorems in real analysis by Constructivism (mathematics), constructive methods. Life Errett Bishop's father, Albert T. Bishop, graduated from the United States Military Academy at West Point, ending his career as professor of mathematics at Wichita State University in Kansas. Although he died when Errett was less than 4 years old, he influenced Errett's eventual career by the math texts he left behind, which is how Errett discovered mathematics. Errett grew up in Newton, Kansas. Errett and his sister were apparent math prodigies. Bishop entered the University of Chicago in 1944, obtaining both the BS and MS in 1947. The doctoral studies he began in that year were interrupted by two years in the US Army, 1950� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton, Kansas
Newton is a city in and the county seat of Harvey County, Kansas, United States. As of the 2020 census, the population of the city was 18,602. Newton is located north of Wichita. The city of North Newton is located immediately north and exists as a separate political entity. Newton is located at the intersection of Interstate 135, U.S. Route 50, and U.S. Route 81 highways. History 19th century For millennia, the land now known as Kansas was inhabited by Native Americans. In 1803, most of modern Kansas was secured by the United States as part of the Louisiana Purchase. In 1854, the Kansas Territory was organized, then in 1861 Kansas became the 34th U.S. state. In 1872, Harvey County was founded. In 1871, the Atchison, Topeka and Santa Fe Railway extended a main line from Emporia westward to Newton by July 1871. The town soon became an important railroad shipping point of Texas cattle. The city was founded in 1871 and named after Newton, Massachusetts, home ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
West Point
The United States Military Academy (USMA), also known Metonymy, metonymically as West Point or simply as Army, is a United States service academies, United States service academy in West Point, New York. It was originally established as a fort, since it sits on strategic high ground overlooking the Hudson River with a scenic view, north of New York City. It is the oldest of the five American service academies and educates cadets for Commission (document)#United States, commissioning into the United States Army. The academy was founded in 1802, one year after President Thomas Jefferson directed that plans be set in motion to establish it. It was constructed on site of Fort Clinton (West Point), Fort Clinton on West Point overlooking the Hudson, which Colonial General Benedict Arnold conspired to turn over to the British during the American Revolutionary War, Revolutionary War. The entire central campus is a National Historic Landmark, national landmark and home to scores of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Banach Algebra
In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach space, that is, a normed space that is complete in the metric induced by the norm. The norm is required to satisfy \, x \, y\, \ \leq \, x\, \, \, y\, \quad \text x, y \in A. This ensures that the multiplication operation is continuous. A Banach algebra is called ''unital'' if it has an identity element for the multiplication whose norm is 1, and ''commutative'' if its multiplication is commutative. Any Banach algebra A (whether it has an identity element or not) can be embedded isometrically into a unital Banach algebra A_e so as to form a closed ideal of A_e. Often one assumes ''a priori'' that the algebra under consideration is unital: for one can develop much of the theory by considering A_e and then applying the outcome in the o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Algebra
In functional analysis, a uniform algebra ''A'' on a compact Hausdorff topological space ''X'' is a closed (with respect to the uniform norm) subalgebra of the C*-algebra ''C(X)'' (the continuous complex-valued functions on ''X'') with the following properties: :the constant functions are contained in ''A'' : for every ''x'', ''y'' \in ''X'' there is ''f''\in''A'' with ''f''(''x'')\ne''f''(''y''). This is called separating the points of ''X''. As a closed subalgebra of the commutative Banach algebra ''C(X)'' a uniform algebra is itself a unital commutative Banach algebra (when equipped with the uniform norm). Hence, it is, (by definition) a Banach function algebra. A uniform algebra ''A'' on ''X'' is said to be natural if the maximal ideals of ''A'' are precisely the ideals M_x of functions vanishing at a point ''x'' in ''X''. Abstract characterization If ''A'' is a unital commutative Banach algebra such that , , a^2, , = , , a, , ^2 for all ''a'' in ''A'', then there i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Function Algebra
In functional analysis, a Banach function algebra on a compact Hausdorff space ''X'' is unital subalgebra, ''A'', of the commutative C*-algebra ''C(X)'' of all continuous, complex-valued functions from ''X'', together with a norm on ''A'' that makes it a Banach algebra. A function algebra is said to vanish at a point ''p'' if ''f''(''p'') = 0 for all f\in A . A function algebra separates points if for each distinct pair of points p,q \in X , there is a function f\in A such that f(p) \neq f(q) . For every x\in X define \varepsilon_x(f)=f(x), for f\in A. Then \varepsilon_x is a homomorphism (character) on A, non-zero if A does not vanish at x. Theorem: A Banach function algebra is semisimple (that is its Jacobson radical is equal to zero) and each commutative unital, semisimple Banach algebra is isomorphic (via the Gelfand transform) to a Banach function algebra on its character space (the space of algebra homomorphisms from ''A'' into the complex numbers given the re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marcel Riesz
Marcel Riesz ( hu, Riesz Marcell ; 16 November 1886 – 4 September 1969) was a Hungarian mathematician, known for work on summation methods, potential theory, and other parts of analysis, as well as number theory, partial differential equations, and Clifford algebras. He spent most of his career in Lund ( Sweden). Marcel is the younger brother of Frigyes Riesz, who was also an important mathematician and at times they worked together (see F. and M. Riesz theorem). Biography Marcel Riesz was born in Győr, Austria-Hungary; he was the younger brother of the mathematician Frigyes Riesz. He obtained his PhD at Eötvös Loránd University under the supervision of Lipót Fejér. In 1911, he moved to Sweden upon the invitation of Gösta Mittag-Leffler. From 1911 to 1925 he taught at ''Stockholms högskola'' (now Stockholm University). From 1926 to 1952 he was professor at Lund University. After retiring, he spent 10 years at universities in the United States. He returned to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frigyes Riesz
Frigyes Riesz ( hu, Riesz Frigyes, , sometimes spelled as Frederic; 22 January 1880 – 28 February 1956) was a HungarianEberhard Zeidler: Nonlinear Functional Analysis and Its Applications: Linear monotone operators. Springer, 199/ref> mathematician who made fundamental contributions to functional analysis, as did his younger brother Marcel Riesz. Life and career He was born into a Jewish family in Győr, Austria-Hungary and died in Budapest, Hungary. Between 1911 and 1919 he was a professor at the Franz Joseph University in Kolozsvár, Austria-Hungary. The post-WW1 Treaty of Trianon transferred former Austro-Hungarian territory including Kolozsvár to the Kingdom of Romania, whereupon Kolozsvár's name changed to Cluj and the University of Kolozsvár moved to Szeged, Hungary, becoming the University of Szeged. Then, Riesz was the rector and a professor at the University of Szeged, as well as a member of the Hungarian Academy of Sciences. and the Polish Academy of Learnin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mergelyan's Approximation Theorem
Mergelyan's theorem is a result from approximation by polynomials in complex analysis proved by the Armenian mathematician Sergei Mergelyan in 1951. Statement :Let ''K'' be a compact subset of the complex plane C such that C∖''K'' is connected. Then, every continuous function ''f'' : ''K''\to C, such that the restriction ''f'' to int(''K'') is holomorphic, can be approximated uniformly on ''K'' with polynomials. Here, int(''K'') denotes the interior of ''K''. Mergelyan's theorem also holds for open Riemann surfaces :If ''K'' is a compact set without holes in an open Riemann surface ''X'', then every function in \mathcal (K) can be approximated uniformly on K by functions in \mathcal(X). Mergelyan's theorem does not always hold in higher dimensions (spaces of several complex variables), but it has some consequences. History Mergelyan's theorem is a generalization of the Weierstrass approximation theorem and Runge's theorem. In the case that C∖''K'' is ''not'' co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institute For Advanced Study
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholars, including J. Robert Oppenheimer, Albert Einstein, Hermann Weyl, John von Neumann, and Kurt Gödel, many of whom had emigrated from Europe to the United States. It was founded in 1930 by American educator Abraham Flexner, together with philanthropists Louis Bamberger and Caroline Bamberger Fuld. Despite collaborative ties and neighboring geographic location, the institute, being independent, has "no formal links" with Princeton University. The institute does not charge tuition or fees. Flexner's guiding principle in founding the institute was the pursuit of knowledge for its own sake.Jogalekar. The faculty have no classes to teach. There are no degree programs or experimental facilities at the institute. Research is never contract ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berkeley, California
Berkeley ( ) is a city on the eastern shore of San Francisco Bay in northern Alameda County, California, United States. It is named after the 18th-century Irish bishop and philosopher George Berkeley. It borders the cities of Oakland and Emeryville to the south and the city of Albany and the unincorporated community of Kensington to the north. Its eastern border with Contra Costa County generally follows the ridge of the Berkeley Hills. The 2020 census recorded a population of 124,321. Berkeley is home to the oldest campus in the University of California System, the University of California, Berkeley, and the Lawrence Berkeley National Laboratory, which is managed and operated by the university. It also has the Graduate Theological Union, one of the largest religious studies institutions in the world. Berkeley is considered one of the most socially progressive cities in the United States. History Indigenous history The site of today's City of Berkeley was the te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Miller Institute
The Miller Institute for Basic Research in Science was established on the University of California, Berkeley, campus in 1955 after Adolph C. Miller and his wife, Mary Sprague Miller, made a donation to the university. It was their wish that the donation be used to establish an institute "dedicated to the encouragement of creative thought and conduct of pure science". The Miller Institute sponsors Miller Research Professors, Visiting Miller Professors and Miller Research Fellows. The first appointments of Miller Professors were made in January 1957. In 2008 the institute created the Miller Senior Fellow program. This program is aimed differently, but is still within the institute's general purpose of supporting excellence in science at Berkeley. The Senior Fellow advances that goal by providing selected faculty with significant discretionary research funds as recognition of distinction in scientific research. The first five-year award went to Professor Randy Schekman, illustrati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California
The University of California (UC) is a public land-grant research university system in the U.S. state of California. The system is composed of the campuses at Berkeley, Davis, Irvine, Los Angeles, Merced, Riverside, San Diego, San Francisco, Santa Barbara, and Santa Cruz, along with numerous research centers and academic abroad centers. The system is the state's land-grant university. Major publications generally rank most UC campuses as being among the best universities in the world. Six of the campuses, Berkeley, Davis, Irvine, Los Angeles, Santa Barbara, and San Diego are considered Public Ivies, making California the state with the most universities in the nation to hold the title. UC campuses have large numbers of distinguished faculty in almost every academic discipline, with UC faculty and researchers having won 71 Nobel Prizes as of 2021. The University of California currently has 10 campuses, a combined student body of 285,862 students, 24,400 faculty membe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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