Almost orthogonal series

On Almost Orthogonal Frames

Almost Orthogonal Submatrices of an Orthogonal Matrix

Let t ≥ 1 and let n, M be natural numbers, n < M. Let A = (a i,j) be an n × M matrix whose rows are orthonormal. Suppose that for all j M n · n i=1 a 2 i,j 1/2 ≤ t.

On absolute generalized Norlund summability of double orthogonal series

In the paper [Y. Okuyama, {it On the absolute generalized N"{o}rlund summability of orthogonal series},Tamkang J. Math. Vol. 33, No. 2, (2002), 161-165] the author has found some sufficient conditions under which an orthogonal seriesis summable $|N,p,q|$ almost everywhere. These conditions are expressed in terms of coefficients of the series. It is the purpose ofthis paper to extend this result...

Hidden Subgroup States Are Almost Orthogonal

It is well known that quantum computers can eeciently nd a hidden subgroup H of a nite Abelian group G. This implies that after only a polynomial (in log jGj) number of calls to the oracle function, the states corresponding to diierent candidate subgroups have exponentially small inner product. We show that this is true for noncom-mutative groups also. We present a quantum algorithm which ident...

Orthogonal series density estimation

Orthogonal series density estimation is a powerful nonparametric estimation methodology that allows one to analyze and present data at hand without any prior opinion about shape of an underlying density. The idea of construction of an adaptive orthogonal series density estimator is explained on the classical example of a direct sample from a univariate density. Data-driven estimators, which hav...