A characterization of Riesz-dual sequences which are near-Markushevich bases

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Infinite Dimensional Analysis Quantum Probability and Related Topics Pub Date : 2021-10-08 DOI:10.1142/s021902572150017x

Ali Reza Neisi, M. Asgari

引用次数: 0

Abstract

The concept of Riesz-duals of a frame is a recently introduced concept with broad implications to frame theory in general, as well as to the special cases of Gabor and wavelet analysis. In this paper, we introduce various alternative Riesz-duals, with a focus on what we call Riesz-duals of type I and II. Next, we provide some characterizations of Riesz-dual sequences in Banach spaces. A basic problem of interest in connection with the study of Riesz-duals in Banach spaces is that of characterizing those Riesz-duals which can essentially be regarded as M-basis. We give some conditions under which an Riesz-dual sequence to be an M-basis for [Formula: see text].

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一类接近markushevich碱基的riesz -对偶序列

框架的riesz -对偶概念是最近才提出的概念，对框架理论以及Gabor和小波分析的特殊情况具有广泛的意义。在本文中，我们介绍了各种可选的riesz -dual，重点是我们称之为I型和II型的riesz -dual。其次，我们给出了Banach空间中riesz -对偶序列的一些刻画。Banach空间中riesz -对偶研究的一个基本问题是如何刻画那些本质上可以看作m基的riesz -对偶。我们给出了riesz对偶序列是m基的若干条件[公式:见文]。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Infinite Dimensional Analysis Quantum Probability and Related Topics 数学-统计学与概率论

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： In the past few years the fields of infinite dimensional analysis and quantum probability have undergone increasingly significant developments and have found many new applications, in particular, to classical probability and to different branches of physics. The number of first-class papers in these fields has grown at the same rate. This is currently the only journal which is devoted to these fields. It constitutes an essential and central point of reference for the large number of mathematicians, mathematical physicists and other scientists who have been drawn into these areas. Both fields have strong interdisciplinary nature, with deep connection to, for example, classical probability, stochastic analysis, mathematical physics, operator algebras, irreversibility, ergodic theory and dynamical systems, quantum groups, classical and quantum stochastic geometry, quantum chaos, Dirichlet forms, harmonic analysis, quantum measurement, quantum computer, etc. The journal reflects this interdisciplinarity and welcomes high quality papers in all such related fields, particularly those which reveal connections with the main fields of this journal.