We consider a finite horizon linear discrete time varying system whose input is a random noise with an imprecisely known probability law. The statistical uncertainty is described by a nonnegative parameter a which constrains the anisotropy of the noise as an entropy theoretic measure of deviation of the actual noise distribution from Gaussian white noise laws with scalar covariance matrices. Th...

Let p z be a monic polynomial of degree n with complex coef cients and let q z be its monic factor We prove an asymptotically sharp inequality of the form kqkE C n kpkE where k kE denotes the sup norm on a compact set E in the plane The best constant CE in this inequality is found by potential theoretic methods We also consider applications of the general result to the cases of a disk and a seg...

semilinear stochastic evolution equations with multiplicative l'evy noise are considered‎. ‎the drift term is assumed to be monotone nonlinear and with linear growth‎. ‎unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎we establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎as corollaries of ...

where λ1 ≥ · · · ≥ λn > 0 are the eigenvalues of A. It is a very useful tool to study the inefficiency of the ordinary least-squares estimate with one regressor in the linear model. Watson 1 introduced the ratio of the variance of the best linear unbiased estimator to the variance of the ordinary least-squares estimator. Such a lower bound of this ratio was provided by Kantorovich inequality 1....

in this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~the idea of equivalent quasi-norm families is introduced.~riesz lemma is established in this space.~finally,~we re-define b-s fuzzy norm and prove that it induces a generating space of quasi-norm family.

where B and D are square blocks. We prove the following inequalities for the Schatten q-norm ||.||q , which are sharp when the blocks are of size at least 2× 2: ||A||q ≤ (2 q − 2)||C||q + ||B|| q q + ||D|| q q, 1 ≤ q ≤ 2, and ||A||q ≥ (2 q − 2)||C||q + ||B|| q q + ||D|| q q, 2 ≤ q. These bounds can be extended to symmetric partitionings into larger numbers of blocks, at the expense of no longer...

We adapt the proof for �(L) Wolff inequalities in the case of plate decompositions of paraboloids, to obtain stronger �2(Lp) versions. These are motivated by the study of Bergman projections for tube domains.

Dedicated to our friends Beresford and Velvel on the occasion of their sixtieth birthdays. ABSTRACT We show that a certain matrix norm ratio studied by Parlett has a supremum that is O(p n) when the chosen norm is the Frobenius norm, while it is O(log n) for the 2-norm. This ratio arises in Parlett's analysis of the Cholesky decomposition of an n by n matrix.