Sentence examples for acts on functions from inspiring English sources

acts on functions defined on the entire space R h n.

The same techniques used to prove Theorems 1 3 can be used to obtain Lieb Thirring bounds also when (mathcal {L}) acts on functions defined on unions of intervals and semi-axes.

The main contribution of this paper lies in generalizing this operator in three different ways: to also include matrix-valued potential functions as in Eq. (1.5), to the more general operator in Eq. (1.4), and lastly to settings where the operator acts on functions defined on subsets of the real line.

In this paper, we mainly study the boundedness of unimodular Fourier multipliers with a time parameter e i t p on the modulation spaces where p is a differentiable real-valued function, namely we estimate e i t p under the multiplier norm, denoted by M s, p. The sharpness of s and the regularity lost are also discussed when the multiplier acts on functions in modulation spaces.

The sequence-based evolutionary conservation approaches are based on the presumption that functionally important residues are preferentially conserved during the evolution because natural selection acts on function [21].

Finally we extend the functional E to act on functions with values in (mathbf {R}^{n}).

The aim of this paper is to define functions of several commuting and non-commuting self-adjoint pseudo-differential operators of non-positive order, by means of the H. Weyl formula[formula]Given 1act on functions defined on the euclidean space Rn.

Then (pi _1(g)) acts on the functions (fin V_1=mathbb {F}_p^X) by the rule begin{aligned} pi _1(g)(f)(x)=f x-1).

Various studies have also suggested that PlcR could acts on other functions, including sporulation [35] and biofilm formation [36].

The findings that Ndel1 acts on the functions of intermediate filament protein NF-L [1] and Dyn2 (this study), both mutated in the sensory motor neurodegenerative Charcot-Marie-Tooth disease [55] [58] further highlight his key role in degenerating neurons.

The metaplectic group acts on Gaussian functions in a particularly simple way.