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In [[mathematics|mathematical]] [[abstract harmonic analysis|harmonic analysis]], '''Harish-Chandra's ''Ξ'' function''' is a [[special function|special]] *''a''(''g'') is the element ''a'' in the Iwasawa decomposition ''g''=''nak'' ...

...tle=The approximation of harmonic functions by harmonic polynomials and by harmonic rational functions|journal=Bull. Amer. Math. Soc.|year=1929|volume=35|issue ...ly]] on <math>\partial{K}</math> by (real-valued) [[harmonic polynomial]]s in the real variables {{math|x}} and {{math|y}}.<ref>{{cite book|author=Gameli ...

'''Matsaev's theorem''' is a theorem from [[complex analysis]], which characterizes the [[Entire function#Order and type|order and type] The theorem was proven in 1960 by [[Vladimir Igorevich Matsaev]].<ref>{{cite journal|first1=Wladimir ...

In mathematics, '''Arakelyan's theorem''' is a generalization of [[Mergelyan's ...locally connected.<ref>{{cite book|last1=Gardiner|first1=Stephen J.|title=Harmonic approximation|url=https://archive.org/details/harmonicapproxim00gard_738|ur ...

In [[number theory]] and [[harmonic analysis]], the '''Landsberg–Schaar relation''' (or '''identity''') is the following \frac{1}{\sqrt{p}}\sum_{n=0}^{p-1}\exp\left(\frac{2\pi in^2q}{p}\right)= ...

In [[analytic number theory]], the '''Kuznetsov trace formula''' is an extensi ...he was able to derive estimates for Fourier coefficients of modular forms in cases where [[Pierre Deligne]]'s proof of the [[Weil conjectures]] was not ...

...on]]s, and the theory of [[Distribution (mathematics)|distributions]], and in [[mathematics education]]. She is a professor of mathematics and chair of t ...rvised by [[Cabiria Andreian Cazacu]].{{r|cv}} She completed her doctorate in 1996 from the [[University of Minnesota]]. Her dissertation, ''Layer Potent ...

In the mathematical field of [[mathematical analysis|analysis]], '''quasiregular maps''' are a class of continuous maps between Euclidean ...ite book|author=Yu. G. Reshetnyak|title=Stability theorems in geometry and analysis|publisher=[[Kluwer Academic Publishers|Kluwer]]|year=1994}}</ref> ...

{{Short description|Formula in representation theory}} ...an [[irreducible representation]] of a semisimple complex [[Lie algebra]] in a [[tensor product]] of two [[irreducible representation]]s. ...

In the field of [[mathematical analysis]], a '''general Dirichlet series''' is an [[series (mathematics)|infinite s == Fundamental theorems == ...

...have a certain "gap" between them. Such a power series is "badly behaved" in the sense that it cannot be extended to be an [[analytic function]] anywher :<math>f(z) = \sum_{j \in \mathbf{N}} \alpha_{j} z^{p_{j}}</math> ...

...he work of Radó and Kneser, rediscovered the result with a different proof in 1945. Choquet also generalized the result to the Poisson integral of a home ...be an orientation-preserving homeomorphism of the unit circle |''z''| = 1 in '''C''' and define the Poisson integral of ''f'' by ...

...&nbsp;2. One implementation involves studying a function by decomposing it in terms of functions with localized frequencies, and using the Littlewood–Pal ...further by Polish mathematicians [[A. Zygmund]] and [[J. Marcinkiewicz]] in the 1930s using complex function theory {{harv|Zygmund|2002|loc=chapters XI ...

...lysis]]) as a way of discretizing objects in order to make computations or analysis easier. For example, to study an arbitrary subset of ''A'' of [[Euclidean s ==Dyadic cubes in Euclidean space== ...

...of [[number theory]], [[combinatorics]], [[ergodic theory]] and [[harmonic analysis]]. [[Ben J. Green|Ben Green]] explains arithmetic combinatorics in his review of "Additive Combinatorics" by [[Terence Tao|Tao]] and [[Van H. ...

In mathematics, '''Watson's lemma''', proved by [[G. N. Watson]] (1918, p. 133 ...(t)</math>, where <math>g(t)</math> has an infinite number of derivatives in the neighborhood of <math>t=0</math>, with <math>g(0)\neq 0</math>, and <ma ...

{{short description|On subsets of the integers in which no member of the set is a multiple of any other}} ...omes large. The theorem is named after [[Felix Behrend]], who published it in 1935. ...

...lev mapping''' is a mapping between [[manifold]]s which has [[smoothness]] in some sense. ...|last1=Eells |first1=J. |last2=Lemaire |first2=L. |title=Another Report on Harmonic Maps |journal=Bulletin of the London Mathematical Society |date=September 1 ...

...traveling salesman problem asks for the shortest way to visit every vertex in a finite set with a discrete path, this analytical version may require the ...e must somehow incorporate information about how flat it is when one zooms in on its points at different scales. ...

...w, are relatively rare; however, probability theory is used systematically in [[combinatorics]] via the [[probabilistic method]]. They are particularly u ==Analysis== ...