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Bohr–Favard Inequality
The Bohr–Favard inequality is an inequality appearing in a problem of Harald Bohr on the boundedness over the entire real axis of the integral of an almost-periodic function. The ultimate form of this inequality was given by Jean Favard; the latter materially supplemented the studies of Bohr, and studied the arbitrary periodic function f(x) = \ \sum _ ^ \infty (a _ \cos kx + b _ \sin kx) with continuous derivative f ^ (x) for given constants r and n which are natural numbers. The accepted form of the Bohr–Favard inequality is \, f \, _ \leq K \, f ^ \, _ , \, f \, _ = \max _ , f(x) , , with the best constant K = K (n, r): K = \sup _ \ \, f \, _ . The Bohr–Favard inequality is closely connected with the inequality for the best approximations of a function and its rth derivative by trigonometric polynomials of an order at most n and with the notion of Kolmogorov's width in the class of differentiable functions (cf. Width ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harald Bohr
Harald August Bohr (22 April 1887 – 22 January 1951) was a Danish mathematician and footballer. After receiving his doctorate in 1910, Bohr became an eminent mathematician, founding the field of almost periodic functions. His brother was the Nobel Prize-winning physicist Niels Bohr. He was a member of the Danish national football team for the 1908 Summer Olympics, where he won a silver medal. Biography Bohr was born in 1887 to Christian Bohr, a professor of physiology, from a Lutheran background, and Ellen Adler Bohr, a woman from a wealthy Jewish family of local renown. Harald had a close relationship with his elder brother, which ''The Times'' likened to that between Captain Cuttle and Captain Bunsby in Charles Dickens' '' Dombey and Son''. Mathematical career Like his father and brother before him, in 1904 Bohr enrolled at the University of Copenhagen, where he studied mathematics, obtaining his master's degree in 1909 and his doctorate a year later. Among his tutors wer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean Favard
Jean Favard (28 August 190221 January 1965) was a French mathematician who worked on analysis. Favard was born in Peyrat-la-Nonière. During World War II he was a prisoner of war in Germany. He also was a President of the French Mathematical Society in 1946. He died in La Tronche, aged 62. See also * Favard measure (se * Bohr–Favard inequality (se * Favard inequality (se * Favard constant * Favard–Akhiezer–Krein theorem * Favard interpolation * Favard theorem * Favard problem (se * Favard operators In functional analysis, a branch of mathematics, the Favard operators are defined by: : mathcal_n(f)x) = \frac \sum_^\infty where x\in\mathbb, n\in\mathbb. They are named after Jean Favard. Generalizations A common generalization is: : mathcal_ ... External linksCOMITE DES AMIS DE JEAN-FAVARD*ThLycée Jean Favardis named after him.Favard is mentioned as a prisoner of war. * {{DEFAULTSORT:Favard, Jean 1902 births 1965 deaths Mathematical analysts 20th-century ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Width
Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the International System of Units (SI) system the base unit for length is the metre. Length is commonly understood to mean the most extended dimension of a fixed object. However, this is not always the case and may depend on the position the object is in. Various terms for the length of a fixed object are used, and these include height, which is vertical length or vertical extent, and width, breadth or depth. Height is used when there is a base from which vertical measurements can be taken. Width or breadth usually refer to a shorter dimension when length is the longest one. Depth is used for the third dimension of a three dimensional object. Length is the measure of one spatial dimension, whereas area is a measure of two dimensions (length squa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Encyclopedia Of Mathematics
The ''Encyclopedia of Mathematics'' (also ''EOM'' and formerly ''Encyclopaedia of Mathematics'') is a large reference work in mathematics. Overview The 2002 version contains more than 8,000 entries covering most areas of mathematics at a graduate level, and the presentation is technical in nature. The encyclopedia is edited by Michiel Hazewinkel and was published by Kluwer Academic Publishers until 2003, when Kluwer became part of Springer. The CD-ROM contains animations and three-dimensional objects. The encyclopedia has been translated from the Soviet ''Matematicheskaya entsiklopediya'' (1977) originally edited by Ivan Matveevich Vinogradov and extended with comments and three supplements adding several thousand articles. Until November 29, 2011, a static version of the encyclopedia could be browsed online free of charge online. This URL now redirects to the new wiki incarnation of the EOM. ''Encyclopedia of Mathematics'' wiki A new dynamic version of the encyclopedia is n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CC BY-SA
A Creative Commons (CC) license is one of several public copyright licenses that enable the free distribution of an otherwise copyrighted "work".A "work" is any creative material made by a person. A painting, a graphic, a book, a song/lyrics to a song, or a photograph of almost anything are all examples of "works". A CC license is used when an author wants to give other people the right to share, use, and build upon a work that the author has created. CC provides an author flexibility (for example, they might choose to allow only non-commercial uses of a given work) and protects the people who use or redistribute an author's work from concerns of copyright infringement as long as they abide by the conditions that are specified in the license by which the author distributes the work. There are several types of Creative Commons licenses. Each license differs by several combinations that condition the terms of distribution. They were initially released on December 16, 2002, by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
GFDL
The GNU Free Documentation License (GNU FDL or simply GFDL) is a copyleft license for free documentation, designed by the Free Software Foundation (FSF) for the GNU Project. It is similar to the GNU General Public License, giving readers the rights to copy, redistribute, and modify (except for "invariant sections") a work and requires all copies and derivatives to be available under the same license. Copies may also be sold commercially, but, if produced in larger quantities (greater than 100), the original document or source code must be made available to the work's recipient. The GFDL was designed for manuals, textbooks, other reference and instructional materials, and documentation which often accompanies GNU software. However, it can be used for any text-based work, regardless of subject matter. For example, the free online encyclopedia Wikipedia uses the GFDL (coupled with the Creative Commons Attribution Share-Alike License) for much of its text, excluding text that was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
