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Malgrange–Zerner Theorem
In mathematics, Malgrange–Zerner theorem (named for Bernard Malgrange Bernard Malgrange (born 6 July 1928) is a French mathematician who works on differential equations and singularity theory. He proved the Ehrenpreis–Malgrange theorem and the Malgrange preparation theorem, essential for the classification theor ... and Martin Zerner) shows that a function on \mathbb^n allowing holomorphic extension in each variable separately can be extended, under certain conditions, to a function holomorphic in all variables jointly. This theorem can be seen as a generalization of Bochner's tube theorem to functions defined on tube-like domains whose base is not an open set. Theorem Let :X=\bigcup_^n \mathbb^\times P \times \mathbb^, \textP=\mathbb+i [0,1), and let W= convex hull of X. Let f: X\to \mathbb be a locally bounded function such that f \in C^\infty(X) and that for any fixed point (x_1,\ldots, x_,x_,\ldots,x_n)\in \mathbb^ the function f(x_1,\ldots, x_,z,x_,\ldots,x_n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernard Malgrange
Bernard Malgrange (born 6 July 1928) is a French mathematician who works on differential equations and singularity theory. He proved the Ehrenpreis–Malgrange theorem and the Malgrange preparation theorem, essential for the classification theorem of the elementary catastrophes of René Thom. He received his Ph.D. from Université Henri Poincaré (Nancy 1) in 1955. His advisor was Laurent Schwartz. He was elected to the Académie des sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at the ... in 1988. In 2012 he gave the Łojasiewicz Lecture (on "Differential algebraic groups") at the Jagiellonian University in Kraków. Publications *''Ideals of differentiable functions'' (Oxford University Press, 1966) *''Équations différentielles à coefficients polynomiaux'', Progress in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Zerner
Martin may refer to: Places * Martin City (other) * Martin County (other) * Martin Township (other) Antarctica * Martin Peninsula, Marie Byrd Land * Port Martin, Adelie Land * Point Martin, South Orkney Islands Australia * Martin, Western Australia * Martin Place, Sydney Caribbean * Martin, Saint-Jean-du-Sud, Haiti, a village in the Sud Department of Haiti Europe * Martin, Croatia, a village in Slavonia, Croatia * Martin, Slovakia, a city * Martín del Río, Aragón, Spain * Martin (Val Poschiavo), Switzerland England * Martin, Hampshire * Martin, Kent * Martin, East Lindsey, Lincolnshire, hamlet and former parish in East Lindsey district * Martin, North Kesteven, village and parish in Lincolnshire in North Kesteven district * Martin Hussingtree, Worcestershire * Martin Mere, a lake in Lancashire ** WWT Martin Mere, a wetland nature reserve that includes the lake and surrounding areas * Martin Mill, Kent North America Canada * Rur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bochner's Tube Theorem
In mathematics, Bochner's tube theorem (named for Salomon Bochner) shows that every function holomorphic on a tube domain in \mathbb^n can be extended to the convex hull In geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space ... of this domain. Theorem Let \omega \subset \mathbb^n be a connected open set. Then every function f(z) holomorphic on the tube domain \Omega = \omega+i \mathbb^n can be extended to a function holomorphic on the convex hull \operatorname(\Omega). A classic reference is (Theorem 9). See also for other proofs. Generalizations The generalized version of this theorem was first proved by Kazlow (1979), also proved by Boivin and Dwilewicz (1998). under more less complicated hypothese. Theorem Let \omega be a connected submanifold of \mathbb^n of class-C^2. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henry Epstein
Henry may refer to: People *Henry (given name) * Henry (surname) * Henry Lau, Canadian singer and musician who performs under the mononym Henry Royalty * Portuguese royalty ** King-Cardinal Henry, King of Portugal ** Henry, Count of Portugal, Henry of Burgundy, Count of Portugal (father of Portugal's first king) ** Prince Henry the Navigator, Infante of Portugal ** Infante Henrique, Duke of Coimbra (born 1949), the sixth in line to Portuguese throne * King of Germany **Henry the Fowler (876–936), first king of Germany * King of Scots (in name, at least) ** Henry Stuart, Lord Darnley (1545/6–1567), consort of Mary, queen of Scots ** Henry Benedict Stuart, the 'Cardinal Duke of York', brother of Bonnie Prince Charlie, who was hailed by Jacobites as Henry IX * Four kings of Castile: ** Henry I of Castile ** Henry II of Castile ** Henry III of Castile ** Henry IV of Castile * Five kings of France, spelt ''Henri'' in Modern French since the Renaissance to italianize the na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
