Sentence examples for using the factorization theorem from inspiring English sources

The deformable models are learnt using the factorization theorem for nonrigid 3D models.

Certain kinds of matrix-valued functions can be factorized using the Potapov factorization theorem.

The presented results can be obtained also using the factorization over the σ-ideal of weakly empty sets.

The procedure we use assumes that the given transfer function (T z)) has a specific form guaranteed by the factorization theorem (see Eq. (15) in Section 5.1).

As an application of this result the factorization theorem is extended to some weighted Bergman spaces.

The Euclidean algorithm for arbitrary n Laurent polynomials and the factorization theorem of polyphase matrices of wavelet bi-frames are proposed.

The norm estimates in the Factorization Theorem of this paper are sharpened to their best possible form by essential improvements in the proof.

We examine the form of the singular term in the factorization theorem and notice that its determinant becomes large when (Re z) to-infty).

In particular, Da Prato and Zabczyk [6] studied the problem (1.1) by the semigroup method, based on the classical fixed point theorem, and used the factorization method to get an estimation of the stochastic convolution, which is a generalization of maximal inequality of martingales to stochastic convolution, and plays an important role in the following sections.

Using Riesz Factorization theorem and Vitali's convergence theorem, Shapiro and Taylor showed in[29] that, C ϕ is compact on H p, for some 0 < p < ∞ if and only if C ϕ is compact on H2.

Using Bourgain's factorization theorem, we characterize the subspaces of Hp, 1⩽p⩽∞, that coincide with the kernels of Toeplitz operators.