Relative asymptotics for orthogonal matrix polynomials with respect to a perturbed matrix measure on the unit circle

19 pages, no figures.-- MSC2000 codes: 42C05, 47A56.MR#: MR1970413 (2004b:42058)Zbl#: Zbl 1047.42021Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of L_n(\tilde{\Omega}) L_n(\Omega) -1} and \Phi_n(z, \tilde{\Omega}) \Phi_n(z, \tilde{\Omega}) -1} where $\tilde{\Omega}(z) = \Omega(z) + M \delta ( z - w)$, $1$, M is a positive definite matrix and δ is the Dirac matrix measure. Here, Ln(·) means the leading coefficient of the orthonormal matrix polynomials Φn(z; •).Finally, we deduce the asymptotic behavior of $\Phi_n(omega, \tilde{\Omega}) \Phi_n(omega, \Omega)$ in the case when M=I.The work of the second author was supported by Dirección General de Enseñanza Superior (DGES) of Spain under grant PB96-0120-C03-01 and INTAS Project INTAS93-0219 Ext.Publicad

Fisher type inequalities for Euclidean t-designs

The notion of a Euclidean t-design is analyzed in the framework of appropriate inner product spaces of polynomial functions. Some Fisher type inequalities are obtained in a simple manner by this method. The same approach is used to deal with certain analogous combinatorial designs

Discrete prolate spheroidal wave functions and interpolation.

The authors describe an algorithm for the interpolation of burst errors in discrete-time signals that can be modeled as being band-limited. The algorithm correctly restores a mutilated signal that is indeed band-limited. The behavior of the algorithm when applied to signals containing noise or out-of-band components can be analyzed satisfactorily with the aid of asymptotic properties of the discrete prolate spheroidal sequences and wave functions. The effect of windowing can also be described conveniently in terms of these sequences and functions

On the (23,14,5) Wagner code

No abstrac

Spherical codes and designs

No abstract