absolutely continuous operator

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English-Russian scientific dictionary. 2008.

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  • Almost Mathieu operator — In mathematical physics, the almost Mathieu operator arises in the study of the quantum Hall effect. It is given by: [H^{lambda,alpha} omega u] (n) = u(n+1) + u(n 1) + 2 lambda cos(2pi (omega + nalpha)) u(n), , acting as a self adjoint operator… …   Wikipedia

  • Integration by parts operator — In mathematics, an integration by parts operator is a linear operator used to formulate integration by parts formulae; the most interesting examples of integration by parts operators occur in infinite dimensional settings and find uses in… …   Wikipedia

  • Nuclear operator — In mathematics, a nuclear operator is roughly a compact operator for which a trace may be defined, such that the trace is finite and independent of the choice of basis (at least on well behaved spaces; there are some spaces on which nuclear… …   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

  • Decomposition of spectrum (functional analysis) — In mathematics, especially functional analysis, the spectrum of an operator generalizes the notion of eigenvalues. Given an operator, it is sometimes useful to break up the spectrum into various parts. This article discusses a few examples of… …   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

  • 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

  • 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

  • Extensions of symmetric operators — In functional analysis, one is interested in extensions of symmetric operators acting on a Hilbert space. Of particular importance is the existence, and sometimes explicit constructions, of self adjoint extensions. This problem arises, for… …   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

  • Sobolev space — In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp norms of the function itself as well as its derivatives up to a given order. The derivatives are understood in a suitable weak sense… …   Wikipedia

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