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...name=Yu/> Asymptotic dimension has important applications in [[geometric analysis]] and [[index theory]]. We then define the ''asymptotic dimension'' <math> \operatorname{asdim}(X)</math> as the smallest integer < ...

In [[mathematics]], an '''ultralimit''' is a geometric construction that assigns a limit [[metric space]] to a sequence of metric ...classes of fundamental groups of 3-manifolds'', [[Geometric and Functional Analysis]], Vol. 5 (1995), no. 3, pp. 582&ndash;603</ref> ...

...1071374|last1=Böttcher|first1=Albrecht|last2=Silbermann|first2=Bernd|title=Analysis of Toeplitz operators|publisher=Springer-Verlag|location=Berlin|year=1990|i ...the [[geometric mean]] of <math>w</math> (well-defined by the [[arithmetic-geometric mean inequality]]). ...

In [[functional analysis]], a branch of mathematics, the '''distortion problem''' is to determine by *{{citation |chapter=Distortion and asymptotic structure |first1=E. |last1=Odell |author-link1=Edward Odell |first2=Th. |l ...

...is a Romanian mathematician notable for her contributions in the area of [[geometric group theory]].<ref name="CDHP">{{cite web|url=http://people.maths.ox.ac.uk ...[[Whitehead Prize]] by the [[London Mathematical Society]] for her work in geometric group theory.<ref>{{cite web|url=http://www.lms.ac.uk/activities/prizes_com ...

...icial]] [[Filtration (mathematics)|filtration]] used in [[topological data analysis]] for analyzing the shape of [[point cloud]] data. It is a multiparameter e It is standard practice in [[topological data analysis]] (TDA) to associate a sequence of nested [[simplicial complex]]es to a fin ...

...io decreases. If we observe <math>\gamma = 1</math> this model becomes a [[geometric Brownian motion]] as in the [[Black-Scholes model]], whereas if <math>\gamm *[https://ssrn.com/abstract=1850709 Asymptotic Approximations to CEV and SABR Models] ...

The geometric meaning of this invariant can be realized within the quantum phase space. < ...tegrability |url=https://www.jstor.org/stable/43666974 |journal=Applicable Analysis and Discrete Mathematics |volume=2 |issue=2 |pages=123–145 |issn=1452-8630} ...

...right at the [[Vector (geometric)#Representations|vector]] origin, a long asymptotic tail, and on the left (forming the arrow head) two (often dense) patches of ...uth, D. & Marchetti, A. (2011). Microbial Assemblage Normalized Transcript Analysis. R package version 0.9.5.</ref> ...

...orm an important class of [[Group (mathematics)|groups]] of interest for [[geometric group theory]]. The main purpose in their study is to extend the theory of ...springer.com/article/10.1007/s000390050075 |journal=Geometric & Functional Analysis |language=en |volume=8 |issue=5 |pages=810–840 |doi=10.1007/s000390050075 | ...

...derandomize a variation of the Clarkson and Shor algorithm, with the same asymptotic runtime.{{r|ramos}} | title = Average case analysis of dynamic geometric optimization ...

In the mathematical subject of [[geometric group theory]], a '''Dehn function''', named after [[Max Dehn]], is an opti ...tric and Dehn functions quickly developed into a separate major theme in [[geometric group theory]], especially since the growth types of these functions are na ...

Small is defined in terms of asymptotic density. === Asymptotic density === ...

one looks for asymptotic solutions of the form The analysis was later generalized by Alì and Hunter,<ref name="AH06">{{harvtxt|Alì|Hunt ...

The joint spectral radius of a set of matrices is the maximal asymptotic growth rate of products of matrices taken in that set. For a finite (or mo ...infinite products of matrices and fractals." SIAM Journal of Mathematical Analysis, 23, pp. 1031–1079, 1992.</ref> A wide number of applications have been pr ...

In the mathematical subject of [[geometric group theory]], an '''acylindrically hyperbolic group''' is a [[group (math ...y generated acylindrically hyperbolic group has cut points in all of its [[asymptotic cone]]s.<ref>{{cite journal |first=A. |last=Sisto |title=Quasi-convexity of ...

...t2=Hirsch |first2=Christian |date=2022-12-22 |title=On the consistency and asymptotic normality of multiparameter persistent Betti numbers |url=https://link.spri ...hy, “[https://donsheehy.net/sheehy12multicover.html A multicover nerve for geometric inference],” in ''CCCG: Canadian conference in computational geometry'', 20 ...

{{Short description|Concept in mathematical analysis}} In [[mathematical analysis]], the '''Dirichlet kernel''', named after the [[Germany|German]] [[mathema ...

...lent.<ref>{{cite book| last = Heinonen| first = Juha | title = Lectures on Analysis on Metric Spaces | series = Universitext | publisher = Springer-Verlag | lo A [[Monotone map#Monotonicity in functional analysis|monotone map]] ''f'':''H''&nbsp;→&nbsp;''H'' on a [[Hilbert space]] ''H'' i ...

...eason Stallings' theorem is considered to be one of the first results in [[geometric group theory]]. ...]s that are not accessible.<ref>M. J. Dunwoody. ''An inaccessible group''. Geometric group theory, Vol. 1 (Sussex, 1991), pp. 75&ndash;78, London Mathematical S ...