A note on mean square spline approximation

Thomson’s Theorem on Mean Square Polynomial Approximation

In 1991, J. E. Thomson determined completely the structure of H2(μ), the closed subspace of L2(μ) that is spanned by the polynomials, whenever μ is a compactly supported measure in the complex plane. As a consequence he was able to show that if H2(μ) = L2(μ), then every function f ∈ H2(μ) admits an analytic extension to a fixed open set Ω, thereby confirming in this context a phenomenon noted e...

A Note on the Mean - Square Quantization Error

This report summarizes the understanding I have gained in my studies for the independent studies course ENEE 699 up to 15th April, 2000. It includes the derivation of an extension of a result of Wong and Brockett on the behaviour of scalar quantizers. 1 Control under limited communication Let, ẋ(t) = f(x(t), u(t)) + n(t) (1) be a controlled dynamical system where the state x(·) ∈ R, the control...

A Note on the Approximation of Mean-Payoff Games

We consider the problem of designing approximation schemes for the values of mean-payoff games. It was recently shown that (1) mean-payoff with rational weights scaled on [−1, 1] admit additive fully-polynomial approximation schemes, and (2) mean-payoff games with positive weights admit relative fully-polynomial approximation schemes. We show that the problem of designing additive/relative appr...

A Note on Character Square

We study the finite groups with an irreducible character χ satisfying the following hypothesis: χ2 has exactly two distinct irreducible constituents, and one of which is linear, and then obtain a result analogous to the Zhmud’s ([8]).

A Note on Square Totients