Wirtinger's Inequality (other)
Wirtinger's inequality is either of two inequalities named after Wilhelm Wirtinger: * Wirtinger's inequality for functions * Wirtinger inequality (2-forms) : ''For other inequalities named after Wirtinger, see Wirtinger's inequality.'' In mathematics, the Wirtinger inequality for 2-forms, named after Wilhelm Wirtinger, states that on a Kähler manifold , the exterior th power of the symplectic fo ...

Inequality (mathematics)
In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size. There are several different notations used to represent different kinds of inequalities: * The notation ''a'' ''b'' means that ''a'' is greater than ''b''. In either case, ''a'' is not equal to ''b''. These relations are known as strict inequalities, meaning that ''a'' is strictly less than or strictly greater than ''b''. Equivalence is excluded. In contrast to strict inequalities, there are two types of inequality relations that are not strict: * The notation ''a'' ≤ ''b'' or ''a'' ⩽ ''b'' means that ''a'' is less than or equal to ''b'' (or, equivalently, at most ''b'', or not greater than ''b''). * The notation ''a'' ≥ ''b'' or ''a'' ⩾ ''b'' means that ''a'' is greater than or equal to ''b'' (or, equivalently, at least ''b'', or not less than ''b''). The r ...
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Wilhelm Wirtinger
Wilhelm Wirtinger (19 July 1865 – 16 January 1945) was an Austrian mathematician, working in complex analysis, geometry, algebra, number theory, Lie groups and knot theory. Biography He was born at Ybbs on the Danube and studied at the University of Vienna, where he received his doctorate in 1887, and his habilitation in 1890. Wirtinger was greatly influenced by Felix Klein with whom he studied at the University of Berlin and the University of Göttingen. Honours In 1907 the Royal Society of London awarded him the Sylvester Medal, for his contributions to the general theory of functions. Work Research activity He worked in many areas of mathematics, publishing 71 works. His first significant work, published in 1896, was on theta functions. He proposed as a generalization of eigenvalues, the concept of the spectrum of an operator, in an 1897 paper; the concept was further extended by David Hilbert and now it forms the main object of investigation in the field of spectral ...
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Wirtinger's Inequality For Functions
: ''For other inequalities named after Wirtinger, see Wirtinger's inequality.'' In the mathematical field of analysis, the Wirtinger inequality is an important inequality for functions of a single variable, named after Wilhelm Wirtinger. It was used by Adolf Hurwitz in 1901 to give a new proof of the isoperimetric inequality for curves in the plane. A variety of closely related results are today known as Wirtinger's inequality, all of which can be viewed as certain forms of the Poincaré inequality. Theorem There are several inequivalent versions of the Wirtinger inequality: * Let be a continuous and differentiable function on the interval with average value zero and with . Then ::\int_0^L y(x)^2\,\mathrmx\leq\frac\int_0^L y'(x)^2\,\mathrmx, : and equality holds if and only if for some numbers and . * Let be a continuous and differentiable function on the interval with . Then ::\int_0^L y(x)^2\,\mathrmx\leq\frac\int_0^L y'(x)^2\,\mathrmx, : and equality holds if and only if ...
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