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uniformly bounded series

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  • Series (mathematics) — A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely.[1] In mathematics, given an infinite sequence of numbers { an } …   Wikipedia

  • Bounded mean oscillation — In harmonic analysis, a function of bounded mean oscillation, also known as a BMO function, is a real valued function whose mean oscillation is bounded (finite). The space of functions of bounded mean oscillation (BMO), is a function space that,… …   Wikipedia

  • Volterra series — The Volterra series and Volterra theorem was developed in 1887 by Vito Volterra. It is a model for non linear behavior, similar to the Taylor series. It differs from the Taylor series in its ability to capture memory effects. The Taylor series… …   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

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

  • Laurent series — A Laurent series is defined with respect to a particular point c and a path of integration γ. The path of integration must lie in an annulus (shown here in red) inside of which f(z) is holomorphic (analytic). In mathematics, the Laurent series of …   Wikipedia

  • Modulus of continuity — In mathematical analysis, a modulus of continuity is a function used to measure quantitatively the uniform continuity of functions. So, a function admits ω as a modulus of continuity if and only if for all x and y in the domain of f. Since moduli …   Wikipedia

  • Helly's selection theorem — In mathematics, Helly s selection theorem states that a sequence of functions that is locally of bounded total variation and uniformly bounded at a point has a convergent subsequence. In other words, it is a compactness theorem for the space… …   Wikipedia

  • Zonal spherical function — In mathematics, a zonal spherical function or often just spherical function is a function on a locally compact group G with compact subgroup K (often a maximal compact subgroup) that arises as the matrix coefficient of a K invariant vector in an… …   Wikipedia

  • Dominated convergence theorem — In measure theory, Lebesgue s dominated convergence theorem provides sufficient conditions under which two limit processes commute, namely Lebesgue integration and almost everywhere convergence of a sequence of functions. The dominated… …   Wikipedia

  • Boundedly generated group — In mathematics, a group is called boundedly generated if it can be expressed as a finite product of cyclic subgroups. The property of bounded generation is also closely related with the congruence subgroup problem (see harvnb|Lubotzky|Segal|2003) …   Wikipedia

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