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Peter Duren
Peter Larkin Duren (30 April 1935, New Orleans, Louisiana – July 10, 2020) was an American mathematician. He specialized in mathematical analysis and was known for the monographs and textbooks he has written. Academic Career Duren received in 1956 his bachelor's degree from Harvard University and in 1960 his PhD from Massachusetts Institute of Technology, MIT under Gian-Carlo Rota with thesis ''Spectral theory of a class of non-selfadjoint infinite matrix operators''. As a postdoc he was an instructor at Stanford University. At the University of Michigan, he became in 1962 an assistant professor, in 1966 an associate professor, in 1969 a professor, and in 2010 a professor emeritus. Duren was in 1968/69 at the Institute for Advanced Study, in 1975 a visiting professor at the Technion in Haifa, in 1964/65 a visiting scientist at Imperial College London, Imperial College and the University of Paris-Sud in Orsay, in 1982 a visiting professor at the University of Maryland and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New Orleans, Louisiana
New Orleans ( , ,New Orleans Merriam-Webster. ; french: La Nouvelle-Orléans , es, Nueva Orleans) is a Consolidated city-county, consolidated city-parish located along the Mississippi River in the southeastern region of the U.S. state of Louisiana. With a population of 383,997 according to the 2020 U.S. census, it is the List of municipalities in Louisiana, most populous city in Louisiana and the twelfth-most populous city in the southeastern United States. Serving as a List of ports in the United States, major port, New Orleans is considered an economic and commercial hub for the broader Gulf Coast of the United States, Gulf Coast region of the United States. New Orleans is world-renowned for its Music of New Orleans, distinctive music, Louisiana Creole cuisine, Creole cuisine, New Orleans English, uniq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Witwatersrand
The University of the Witwatersrand, Johannesburg (), is a multi-campus South African public research university situated in the northern areas of central Johannesburg. It is more commonly known as Wits University or Wits ( or ). The university has its roots in the mining industry, as do Johannesburg and the Witwatersrand in general. Founded in 1896 as the South African School of Mines in Kimberley, it is the third oldest South African university in continuous operation. The university has an enrolment of 40,259 students as of 2018, of which approximately 20 percent live on campus in the university's 17 residences. 63 percent of the university's total enrolment is for undergraduate study, with 35 percent being postgraduate and the remaining 2 percent being Occasional Students. The 2017 Academic Ranking of World Universities (ARWU) places Wits University, with its overall score, as the highest ranked university in Africa. Wits was ranked as the top university in South Africa in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Special Function
Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defined by consensus, and thus lacks a general formal definition, but the List of mathematical functions contains functions that are commonly accepted as special. Tables of special functions Many special functions appear as solutions of differential equations or integrals of elementary functions. Therefore, tables of integrals usually include descriptions of special functions, and tables of special functions include most important integrals; at least, the integral representation of special functions. Because symmetries of differential equations are essential to both physics and mathematics, the theory of special functions is closely related to the theory of Lie groups and Lie algebras, as well as certain topics in mathematical physics. Symbolic co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Potential Theory
In mathematics and mathematical physics, potential theory is the study of harmonic functions. The term "potential theory" was coined in 19th-century physics when it was realized that two fundamental forces of nature known at the time, namely gravity and the electrostatic force, could be modeled using functions called the gravitational potential and electrostatic potential, both of which satisfy Poisson's equation—or in the vacuum, Laplace's equation. There is considerable overlap between potential theory and the theory of Poisson's equation to the extent that it is impossible to draw a distinction between these two fields. The difference is more one of emphasis than subject matter and rests on the following distinction: potential theory focuses on the properties of the functions as opposed to the properties of the equation. For example, a result about the singularities of harmonic functions would be said to belong to potential theory whilst a result on how the solution depends ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Function Theory
Geometric function theory is the study of geometric properties of analytic functions. A fundamental result in the theory is the Riemann mapping theorem. Topics in geometric function theory The following are some of the most important topics in geometric function theory: Conformal maps A conformal map is a function which preserves angles locally. In the most common case the function has a domain and range in the complex plane. More formally, a map, : f: U \rightarrow V\qquad with U,V \subset \mathbb^n is called conformal (or angle-preserving) at a point u_0 if it preserves oriented angles between curves through u_0 with respect to their orientation (i.e., not just the magnitude of the angle). Conformal maps preserve both angles and the shapes of infinitesimally small figures, but not necessarily their size or curvature. Quasiconformal maps In mathematical complex analysis, a quasiconformal mapping, introduced by and named by , is a homeomorphism between plane domains whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harmonic Analysis
Harmonic analysis is a branch of mathematics concerned with the representation of Function (mathematics), functions or signals as the Superposition principle, superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an extended form of Fourier analysis). In the past two centuries, it has become a vast subject with applications in areas as diverse as number theory, representation theory, signal processing, quantum mechanics, tidal analysis and neuroscience. The term "harmonics" originated as the Ancient Greek word ''harmonikos'', meaning "skilled in music". In physical eigenvalue problems, it began to mean waves whose frequencies are Multiple (mathematics), integer multiples of one another, as are the frequencies of the Harmonic series (music), harmonics of music notes, but the term has been generalized beyond its original meaning. The classical Fourier transform on R''n'' is still an area of ongoing research, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Branges's Theorem
In complex analysis, de Branges's theorem, or the Bieberbach conjecture, is a theorem that gives a necessary condition on a holomorphic function in order for it to map the open unit disk of the complex plane injectively to the complex plane. It was posed by and finally proven by . The statement concerns the Taylor coefficients a_n of a univalent function, i.e. a one-to-one holomorphic function that maps the unit disk into the complex plane, normalized as is always possible so that a_0=0 and a_1=1. That is, we consider a function defined on the open unit disk which is holomorphic and injective ('' univalent'') with Taylor series of the form :f(z)=z+\sum_ a_n z^n. Such functions are called ''schlicht''. The theorem then states that : , a_n, \leq n \quad \textn\geq 2. The Koebe function (see below) is a function in which a_n=n for all n, and it is schlicht, so we cannot find a stricter limit on the absolute value of the nth coefficient. Schlicht functions The normalizations : ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hardy Space
In complex analysis, the Hardy spaces (or Hardy classes) ''Hp'' are certain spaces of holomorphic functions on the unit disk or upper half plane. They were introduced by Frigyes Riesz , who named them after G. H. Hardy, because of the paper . In real analysis Hardy spaces are certain spaces of distributions on the real line, which are (in the sense of distributions) boundary values of the holomorphic functions of the complex Hardy spaces, and are related to the ''Lp'' spaces of functional analysis. For 1 ≤ ''p'' < ∞ these real Hardy spaces ''Hp'' are certain s of ''Lp'', while for ''p'' < 1 the ''Lp'' spaces have some undesirable properties, and the Hardy spaces are much better behaved. There are also higher-dimensional generalizations, consisting of certain holomorphic functions on |
Frederick Gehring
Frederick William Gehring (7 August 1925 – 29 May 2012) was an American mathematician who worked in the area of complex analysis (quasi-conformal mappings). Personal life Both of Fred Gehring's parents graduated from the University of Michigan. His father, Carl Ernst Gehring, was a journalist who worked for the Ann Arbor News and a music critic. His mother, Hester Reed Gehring, was a foreign language examiner for students who needed to prove competency as a requirement for their graduate degree. She was also the daughter of John Oren Reed, a physics professor and Dean of the College of Literature, Science and the Arts at the University of Michigan. Gehring graduated from University High School in 1943 and hoped to attend the Massachusetts Institute of Technology. However, because of World War II, he was about to be drafted into the United States Navy. So he instead enrolled in the V-12 Navy College Training Program at the University of Michigan where he earned ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Festschrift
In academia, a ''Festschrift'' (; plural, ''Festschriften'' ) is a book honoring a respected person, especially an academic, and presented during their lifetime. It generally takes the form of an edited volume, containing contributions from the honoree's colleagues, former pupils, and friends. ''Festschriften'' are often titled something like ''Essays in Honour of...'' or ''Essays Presented to... .'' Terminology The term, borrowed from German, and literally meaning 'celebration writing' (cognate with ''feast-script''), might be translated as "celebration publication" or "celebratory (piece of) writing". An alternative Latin term is (literally: 'book of friends'). A comparable book presented posthumously is sometimes called a (, 'memorial publication'), but this term is much rarer in English. A ''Festschrift'' compiled and published by electronic means on the internet is called a (pronounced either or ), a term coined by the editors of the late Boris Marshak's , ''Eran ud Aner ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America. The ''American Mathematical Monthly'' is an expository journal intended for a wide audience of mathematicians, from undergraduate students to research professionals. Articles are chosen on the basis of their broad interest and reviewed and edited for quality of exposition as well as content. In this the ''American Mathematical Monthly'' fulfills a different role from that of typical mathematical research journals. The ''American Mathematical Monthly'' is the most widely read mathematics journal in the world according to records on JSTOR. Tables of contents with article abstracts from 1997–2010 are availablonline The MAA gives the Lester R. Ford Awards annually to "authors of articles of expository excellence" published in the ''American Mathematical Monthly''. Editors *2022– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michigan Mathematical Journal
The ''Michigan Mathematical Journal'' (established 1952) is published by the mathematics department at the University of Michigan. An important early editor for the Journal was George Piranian. Historically, the Journal has been published a small number of times in a given year (currently four), in all areas of mathematics. The current Managing Editor is Mircea Mustaţă Mircea is a Romanian masculine given name, a form of the South Slavic name Mirče (Мирче) that derives from the Slavic word ''mir'', meaning 'peace'. It may refer to: People Princes of Wallachia * Mircea I of Wallachia (1355–1418), a .... References External links * Mathematics journals University of Michigan 1952 establishments in Michigan Publications established in 1952 {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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