Sentence examples for bound on the norm from inspiring English sources

In this paper we prove that the bound on the norm of the dyadic paraproduct in the weighted Lebesgue space L2(w) depends linearly on the Ad2 characteristic of the weight w using Bellman function techniques and extrapolate this result to the Lp(w) case.

The error between the approximate and exact solutions is given, and an upper bound on the norm of the error in terms of a measure of the rate of change of the system matrix and the norm of the exact solution of the system is derived.

If for an integer d, Hd denotes the subspace of the von Neumann algebra of a free group FI spanned by the words of length d in the generators (but not their inverses), then we provide in this paper an explicit upper bound on the norm on Mn(Hd), which improves and generalizes previous results by Kemp Speicher (in the scalar case) and Buchholz and Parcet Pisier (in the non-holomorphic setting).

Furthermore, using an Implicit function theorem, we get a bound on the norm of this gradient.

The following upper bound on the norm of the inverse R − 1 can be found in the work of Albeverio, Makarov, and Motovilov [[7], Theorem 2.7].

It is known that such is ensured by imposing a bound on the norm of the Girsanov kernels from the risk-neutral pricing measures.

Specifically, an upper bound on this norm, the ★-norm, is minimized, which, unlike the 1-norm, can be formulated in terms of linear and bilinear matrix inequalities.

We utilize a particular solution of the Bounded Real Lemma that provides an explicit upper bound on the H∞ norm of a collocated structural system.

For a given set of linear feedback gains, a given switching scheme and a given bound on the L2 norm of the disturbances, conditions are established in terms of linear or bilinear matrix inequalities under which the resulting switched system is bounded state stable, that is, trajectories starting from a bounded set will remain inside the set or a larger bounded set.

Next we derive a bound on the L2 norm of the approximation error of (2.1).

The following proposition gives a bound on the Hilbert Schmidt norm.