Changzhong Zhu

On the completeness of the system { Zτ n } in L 2

Given an unbounded domain ? located outside an angle domain with vertex at the origin, and a sequence of distinct complex numbers {?n} (n=1,2,?) satisfyingn??n? ?D as n?∞ with 0

On the Completeness of the System {Z-n} in L2

Given an unbounded domain ? located outside an angle domain with vertex at the origin, and a sequence of distinct complex numbers {?n} (n=1,2,?) satisfyingn??n? ?D as n?∞ with 0

Solving equations nonlinear in only one of N + 1 variables

Equations linear in n out of n + 1 variables can be solved by reduction to a linear subproblem and variation of the nonlinear parameter.

An algorithm for discrete nonlinear biased approximation

For approximating functions with an alternating characterization of best Chebyshev approximations, a (single-point exchange) Remez algorithm is used to obtain the best biased approximation on a finite set. This is useful for one-sided approximation.

Bi-orthogonal Expansions in the Space L 2(0,∞)

In this paper we deduce bi-orthogonal expansions in the space L 2(0,∞) with respect to two special systems of functions from the corresponding expansions in the Hardy space \(H^{2}_{+}\) for the upper half-plane.

The Growth of an Entire Function and its Dirichlet Coefficients and Exponents

Let F be an entire function represented by a (generalized) Dirichlet series where the coefficients { d n } and exponents { n } ( n = 1, 2, …) are sequences of complex numbers. We introduce a modified (R)-order 𝜌 and modified (R)-type σ and we obtain an estimate for | d n | when n is sufficiently large in terms of 𝜌 , σ and n . Other estimates relating 𝜌 and σ to { n } and { d n } are also obtained.

Generalized strong unicity constants in linear uniform approximation

For linear best uniform approximation, we introduce the generalized strong unicity constant, study its characterizations and obtain a convenient computation of it. This constant has already been used to tell how near a (linear or nonlinear) parameter is to the best (unknown) parameter in aribitrary parameter norm.

Minimax exponential approximation can be ILL-posed

Published data was slightly perturbed and a minimax approximation by sums of exponentials was computed. This differed substantially from the published approximation.

The remez algorithm for biased uniform approximation on an interval

Uniform approximation on an interval [α β] by an alternating family when positive deviations (errors) are magnified by a bias factor is considered. This problem is related to one-sided uniform approximation from above for large bias factors. Best approximations are characterized by alternation, suggesting use of the first authors variant of the Remez 2nd algorithm for generalized weight functions. Previously written subprograms of the authors are combined with minor modifications to produce a general subprogram for families satisfying the hypotheses of Meinardus and Schwedt.

A limit theorem of discretization with weights large on nodes

Abstract By combining discretization and weighting on nodes, one can in the limit approximate on infinite sets under Lagrange-type interpolatory constraints, enabling the use of existing algorithms and programs.