Sentence examples for dimensional extensions from inspiring English sources
The boundedness of (h_{Phi} (f )) as well as its high dimensional extensions in various function spaces, mainly on Lebesgue and Hardy spaces, has been studied by many authors, for example, [1 5] and [6] are among many others.
We call the operators ˜A symplectic dimensional extensions of A. In this paper we study the relation between A and ˜A in detail, in particular their regularity, invertibility and spectral properties.
The formal infinite dimensional extension of the Sard inequality,μ TA)⩽∫A |Lambda;| dμ,is shown to hold and applications to absolute continuity on Wiener space are presented.
Our approach is a direct infinite dimensional extension of the finite-dimensional feedback linearization/backstepping approaches and employs spatial Volterra series nonlinear operators both in the transformation to a stable linear PDE and in the feedback law.
This is done by employing a method of Putinar and Vasilescu [M. Putinar, F.-H. Vasilescu, Solving moment problems by dimensional extension, Ann. of Math. (2) 1999(3) (1087 1107]–1107] for the corresponding multidimensional moment problem.
In this paper, we implement for the first time a two dimensional extension of the spring-block model, applying it to structured surfaces and investigating by means of numerical simulations the frictional behaviour of a surface in the presence of features like cavities, pillars or complex anisotropic structures.
Some n-dimensional extensions have been recently proposed in the literature.
Focus is presently on two-dimensional vector processes, but higher-dimensional extensions are also established.
It is shown that for amenable groups, all finite-dimensional extensions of Ap(G) algebras split strongly.
It was introduced in [6] to get different types of Pólya-Knopp inequalities, including the n-dimensional extensions of the Levin-Cochran-Lee-type inequalities and Carleson's result.
3) For researchers, which prefer to use information theoretic criteria (ITC) techniques, we have also proposed multi-dimensional extensions of AIC and MDL, called R-D AIC and R-D MDL, respectively.
