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Plancherel
Michel Plancherel (16 January 1885, Bussy, Fribourg4 March 1967, Zurich) was a Swiss mathematician. He was born in Bussy ( Fribourg, Switzerland) and obtained his Diplom in mathematics from the University of Fribourg and then his doctoral degree in 1907 with a thesis written under the supervision of Mathias Lerch. Plancherel was a professor in Fribourg (1911), and from 1920 at ETH Zurich. He worked in the areas of mathematical analysis, mathematical physics and algebra, and is known for the Plancherel theorem in harmonic analysis. He was an Invited Speaker of the ICM in 1924 at TorontoPlancherel, Michel (1924" Sur les séries de fonctions orthogonales." In ''Proceedings of the International Mathematical Congress'', Toronto, vol. 1, pp. 619–622. and in 1928 at Bologna. He was married to Cécile Tercier, had nine children, and presided at the ''Mission Catholique Française'' in Zürich. See also *Plancherel measure In mathematics, Plancherel measure is a measure d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plancherel Theorem For Spherical Functions
In mathematics, the Plancherel theorem for spherical functions is an important result in the group representation, representation theory of semisimple Lie groups, due in its final form to Harish-Chandra. It is a natural generalisation in non-commutative harmonic analysis of the Plancherel formula and Fourier inversion formula in the representation theory of the group of real numbers in classical harmonic analysis and has a similarly close interconnection with the theory of differential equations. It is the special case for zonal spherical functions of the general Plancherel theorem for semisimple Lie groups, also proved by Harish-Chandra. The Plancherel theorem gives the Spectral theory, eigenfunction expansion of radial functions for the Laplacian operator on the associated symmetric space ''X''; it also gives the direct integral, direct integral decomposition into irreducible representations of the regular representation on . In the case of hyperbolic space, these expansions were kn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plancherel Measure
In mathematics, Plancherel measure is a measure defined on the set of irreducible unitary representations of a locally compact group G, that describes how the regular representation breaks up into irreducible unitary representations. In some cases the term Plancherel measure is applied specifically in the context of the group G being the finite symmetric group S_n – see below. It is named after the Swiss mathematician Michel Plancherel for his work in representation theory. Definition for finite groups Let G be a finite group, we denote the set of its irreducible representations by G^\wedge. The corresponding Plancherel measure over the set G^\wedge is defined by :\mu(\pi) = \frac, where \pi\in G^\wedge, and \mathrm\pi denotes the dimension of the irreducible representation \pi. Definition on the symmetric group An important special case is the case of the finite symmetric group S_n, where n is a positive integer. For this group, the set S_n^\wedge of irreducible repre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plancherel Theorem
In mathematics, the Plancherel theorem (sometimes called the Parseval–Plancherel identity) is a result in harmonic analysis, proven by Michel Plancherel in 1910. It states that the integral of a function's squared modulus is equal to the integral of the squared modulus of its frequency spectrum. That is, if f(x) is a function on the real line, and \widehat(\xi) is its frequency spectrum, then A more precise formulation is that if a function is in both Lp spaces L^1(\mathbb) and L^2(\mathbb), then its Fourier transform is in L^2(\mathbb), and the Fourier transform map is an isometry with respect to the ''L''2 norm. This implies that the Fourier transform map restricted to L^1(\mathbb) \cap L^2(\mathbb) has a unique extension to a linear isometric map L^2(\mathbb) \mapsto L^2(\mathbb), sometimes called the Plancherel transform. This isometry is actually a unitary map. In effect, this makes it possible to speak of Fourier transforms of quadratically integrable functions. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michel Plancherel (1932)
Michel Plancherel (16 January 1885 – 4 March 1967) was a Swiss mathematician. He was born in Bussy (Fribourg, Switzerland) and obtained his Diplom in mathematics from the University of Fribourg and then his doctoral degree in 1907 with a thesis written under the supervision of Mathias Lerch. Plancherel was a professor in Fribourg (1911), and from 1920 at ETH Zurich. He worked in the areas of mathematical analysis, mathematical physics and algebra, and is known for the Plancherel theorem in harmonic analysis. He was an Invited Speaker of the ICM in 1924 at TorontoPlancherel, Michel (1924" Sur les séries de fonctions orthogonales." In ''Proceedings of the International Mathematical Congress'', Toronto, vol. 1, pp. 619–622. and in 1928 at Bologna. He was married to Cécile Tercier, had nine children, and presided at the ''Mission Catholique Française'' in Zürich , neighboring_municipalities = Adliswil, Dübendorf, Fällanden, Kilchberg, Maur, Oberengstringen, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rendiconti Del Circolo Matematico Di Palermo
The Circolo Matematico di Palermo (Mathematical Circle of Palermo) is an Italian mathematical society, founded in Palermo by Sicilian geometer Giovanni B. Guccia in 1884.The Mathematical Circle of Palermo . Retrieved 2011-06-19. It began accepting foreign members in 1888, and by the time of Guccia's death in 1914 it had become the foremost international mathematical society, with approximately one thousand members. However, subsequently to that time it declined in influence. Publications ''Rendiconti del Circolo Matemat ...[...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] |
University Of Fribourg
The University of Fribourg (french: Université de Fribourg; german: Universität Freiburg) is a public university located in Fribourg, Switzerland. The roots of the university can be traced back to 1580, when the notable Jesuit Peter Canisius founded the Collège Saint-Michel in the City of Fribourg. In 1763, an academy of law was founded by the state of Fribourg which formed the nucleus of the present Law Faculty. The University of Fribourg was finally created in 1889 by an Act of the parliament of the Swiss Canton of Fribourg. The University of Fribourg is Switzerland's only bilingual university and offers full curricula in both French and German, two of Switzerland's national languages. Students number about 10,000; there are about 200 tenured professors and 700 other academic teaching and research personnel. The Misericorde Campus, constructed between 1939 and 1942, was designed by the architects Honegger and Dumas, students of Swiss architect Le Corbusier. There are five ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathias Lerch
Mathias Lerch (''Matyáš Lerch'', ) (20 February 1860, Milínov – 3 August 1922, Sušice) was a Czech mathematician who published about 250 papers, largely on mathematical analysis and number theory. He studied in Prague and Berlin, and held teaching positions at the Czech Technical Institute in Prague, the University of Fribourg in Switzerland, the Czech Technical Institute in Brno, and Masaryk University in Brno; he was the first mathematics professor at Masaryk University when it was founded in 1920. In 1900, he was awarded the Grand Prize of the French Academy of Sciences for his number-theoretic work. The Lerch zeta function is named after him, as is the Appell–Lerch sum. His doctoral students include Michel Plancherel and Otakar Borůvka Otakar Borůvka (10 May 1899 in Uherský Ostroh – 22 July 1995 in Brno) was a Czech mathematician best known today for his work in graph theory.. Education and career Borůvka was born in Uherský Ostroh, a town in M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zürich
Zürich () is the list of cities in Switzerland, largest city in Switzerland and the capital of the canton of Zürich. It is located in north-central Switzerland, at the northwestern tip of Lake Zürich. As of January 2020, the municipality has 434,335 inhabitants, the Urban agglomeration, urban area 1.315 million (2009), and the Zürich metropolitan area 1.83 million (2011). Zürich is a hub for railways, roads, and air traffic. Both Zurich Airport and Zürich Hauptbahnhof, Zürich's main railway station are the largest and busiest in the country. Permanently settled for over 2,000 years, Zürich was founded by the Roman Empire, Romans, who called it '. However, early settlements have been found dating back more than 6,400 years (although this only indicates human presence in the area and not the presence of a town that early). During the Middle Ages, Zürich gained the independent and privileged status of imperial immediacy and, in 1519, became a primary centre of the Protestant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Fribourg Alumni
A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, the designation is reserved for colleges that have a graduate school. The word ''university'' is derived from the Latin ''universitas magistrorum et scholarium'', which roughly means "community of teachers and scholars". The first universities were created in Europe by Catholic Church monks. The University of Bologna (''Università di Bologna''), founded in 1088, is the first university in the sense of: *Being a high degree-awarding institute. *Having independence from the ecclesiastic schools, although conducted by both clergy and non-clergy. *Using the word ''universitas'' (which was coined at its foundation). *Issuing secular and non-secular degrees: grammar, rhetoric, logic, theology, canon law, notarial law.Hunt Janin: "The university i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ETH Zurich Faculty
(colloquially) , former_name = eidgenössische polytechnische Schule , image = ETHZ.JPG , image_size = , established = , type = Public , budget = CHF 1.896 billion (2021) , rector = Günther Dissertori , president = Joël Mesot , academic_staff = 6,612 (including doctoral students, excluding 527 professors of all ranks, 34% female, 65% foreign nationals) (full-time equivalents 2021) , administrative_staff = 3,106 (40% female, 19% foreign nationals, full-time equivalents 2021) , students = 24,534 (headcount 2021, 33.3% female, 37% foreign nationals) , undergrad = 10,642 , postgrad = 8,299 , doctoral = 4,460 , other = 1,133 , address = Rämistrasse 101CH-8092 ZürichSwitzerland , city = Zürich , coor = , campus = Urban , language = German, English (Masters and upwards, sometimes Bachelor) , affiliations = CESAER, EUA, GlobalTech, IARU, IDEA League, UNITECH , website ethz.ch, colors = Black and White , logo = ETH Zürich Logo black.svg ETH Züric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Swiss Roman Catholics
Swiss may refer to: * the adjectival form of Switzerland *Swiss people Places *Swiss, Missouri * Swiss, North Carolina *Swiss, West Virginia *Swiss, Wisconsin Other uses *Swiss-system tournament, in various games and sports *Swiss International Air Lines **Swiss Global Air Lines, a subsidiary *Swissair, former national air line of Switzerland *.swiss alternative TLD for Switzerland See also *Swiss made, label for Swiss products *Swiss cheese (other) *Switzerland (other) *Languages of Switzerland, none of which are called "Swiss" *International Typographic Style, also known as Swiss Style, in graphic design *Schweizer (other), meaning Swiss in German *Schweitzer, a family name meaning Swiss in German *Swisse Swisse is a vitamin, supplement, and skincare brand. Founded in Australia in 1969 and globally headquartered in Melbourne, and was sold to Health & Happiness, a Chinese company based in Hong Kong previously known as Biostime International, in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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