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locally integrable function

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  • Locally integrable function — In mathematics, a locally integrable function is a function which is integrable on any compact set of its domain of definition. Formal definition Formally, let Omega be an open set in the Euclidean space scriptstylemathbb{R}^n and scriptstyle… …   Wikipedia

  • Maximal function — Maximal functions appear in many forms in harmonic analysis (an area of mathematics). One of the most important of these is the Hardy–Littlewood maximal function. They play an important role in understanding, for example, the differentiability… …   Wikipedia

  • Hardy-Littlewood maximal function — In mathematics, the Hardy Littlewood maximal operator M is a significant non linear operator used in real analysis and harmonic analysis. It takes a function f (a complex valued and locally integrable function) : f:mathbb{R}^{d} ightarrow… …   Wikipedia

  • Dirac delta function — Schematic representation of the Dirac delta function by a line surmounted by an arrow. The height of the arrow is usually used to specify the value of any multiplicative constant, which will give the area under the function. The other convention… …   Wikipedia

  • Generalized function — In mathematics, generalized functions are objects generalizing the notion of functions. There is more than one recognised theory. Generalized functions are especially useful in making discontinuous functions more like smooth functions, and (going …   Wikipedia

  • Holomorphic function — A rectangular grid (top) and its image under a holomorphic function f (bottom). In mathematics, holomorphic functions are the central objects of study in complex analysis. A holomorphic function is a complex valued function of one or more complex …   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

  • Fourier transform — Fourier transforms Continuous Fourier transform Fourier series Discrete Fourier transform Discrete time Fourier transform Related transforms The Fourier transform is a mathematical operation that decomposes a function into its constituent… …   Wikipedia

  • Distribution (mathematics) — This article is about generalized functions in mathematical analysis. For the probability meaning, see Probability distribution. For other uses, see Distribution (disambiguation). In mathematical analysis, distributions (or generalized functions) …   Wikipedia

  • Lp space — In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p norm for finite dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford Schwartz 1958, III.3),… …   Wikipedia

  • Convolution — For the usage in formal language theory, see Convolution (computer science). Convolution of two square pulses: the resulting waveform is a triangular pulse. One of the functions (in this case g) is first reflected about τ = 0 and then offset by t …   Wikipedia

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