Sentence examples for in the space of functions from inspiring English sources

The study is conducted in the space of functions with bounded variations (BV).

On the one hand, one commonly considers a generalized formulation in the space of functions of bounded variation.

Here, the large rectangle represents the space of functions, with S, the image of the space of spike trains in the space of functions under the filter map represented by the wavy line.

Because S is a subset of the space of functions, it is inevitable that the image of the central spike train in the space of functions is different from the function average.

We note that the eigenvalues of the operator (partial_{tt}-partial_{xx}) in the space of functions (u ( x,t ) ), (2pi/omega )-periodic in time and such that, say, (u ( cdot,t ) in H_{0}^{1} ( 0,pi ) ) for all t, are (-omega^{2}l^{2}+j^{2}), (lin Z), (jgeq1).

However, this represents the center of the data in a larger space, the space of functions, rather than the image in the function space of the space of spike trains.

The first setting was in the Hardy space H2, the space of functions analytic on Δ (see[1]).

Let H∞ denote the space of functions in L∞(dθ2π) that have vanishing negative Fourier coefficients.

By (H_{mathrm{per}}^{sigma}(Omega)), (sigmageq0) we shall indicate the space of functions periodic in the sense of (1.2).

We prove that the convergence of a sequence of functions in the space of measurable functions, with respect to the topology of convergence in measure, implies the convergence -almost everywhere ( denotes the Lebesgue measure) of the sequence of rearrangements.

An attempt has been made to give a criteria to a family of functions defined in the space of analytic functions to be univalent.