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boundedness principle

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  • Uniform boundedness principle — In mathematics, the uniform boundedness principle or Banach–Steinhaus theorem is one of the fundamental results in functional analysis. Together with the Hahn–Banach theorem and the open mapping theorem, it is considered one of the cornerstones… …   Wikipedia

  • Uniform boundedness — In mathematics, bounded functions are functions for which there exists a lower bound and an upper bound, in other words, a constant which is larger than the absolute value of any value of this function. If we consider a family of bounded… …   Wikipedia

  • Convergence of Fourier series — In mathematics, the question of whether the Fourier series of a periodic function converges to the given function is researched by a field known as classical harmonic analysis, a branch of pure mathematics. Convergence is not necessarily a given… …   Wikipedia

  • List of mathematics articles (U) — NOTOC U U duality U quadratic distribution U statistic UCT Mathematics Competition Ugly duckling theorem Ulam numbers Ulam spiral Ultraconnected space Ultrafilter Ultrafinitism Ultrahyperbolic wave equation Ultralimit Ultrametric space… …   Wikipedia

  • Compact operator on Hilbert space — In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite rank operators in the uniform operator topology. As such, results from matrix theory… …   Wikipedia

  • Hilbert space — For the Hilbert space filling curve, see Hilbert curve. Hilbert spaces can be used to study the harmonics of vibrating strings. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It… …   Wikipedia

  • Functional analysis — For functional analysis as used in psychology, see the functional analysis (psychology) article. Functional analysis is the branch of mathematics, and specifically of analysis, concerned with the study of vector spaces and operators acting upon… …   Wikipedia

  • Baire category theorem — The Baire category theorem is an important tool in general topology and functional analysis. The theorem has two forms, each of which gives sufficient conditions for a topological space to be a Baire space. Statement of the theorem *(BCT1) Every… …   Wikipedia

  • Fourier series — Fourier transforms Continuous Fourier transform Fourier series Discrete Fourier transform Discrete time Fourier transform Related transforms …   Wikipedia

  • Dirichlet kernel — In mathematical analysis, the Dirichlet kernel is the collection of functions It is named after Johann Peter Gustav Lejeune Dirichlet. The importance of the Dirichlet kernel comes from its relation to Fourier series. The convolution of Dn(x) with …   Wikipedia

  • Baire space — In mathematics, a Baire space is a topological space which, intuitively speaking, is very large and has enough points for certain limit processes. It is named in honor of René Louis Baire who introduced the concept. Motivation In an arbitrary… …   Wikipedia

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