English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Denote by $\mathcal{W}_1$ the set of complex valued functions of the form$a(z)=\sum_{i=-\infty}^{+\infty}a_iz^i$ which are continuous on the unitcircle, and such that $\sum_{i=-\infty}^{+\infty}|ia_i|<\infty$. We call CQTmatrix a quasi-Toeplitz matrix $A$, associated with a continuous symbol$a(z)\in\mathcal W_1$, of the form $A=T(a)+E$, where$T(a)=(t_{i,j})_{i,j\in\mathbb{Z}^+}$ is the semi-infinite Toeplitz matrix suchthat $t_{i,j}=a_{j-i}$, for $i,j\in\mathbb Z^+$, and$E=(e_{i,j})_{i,j\in\mathbb{Z}^+}$ is a semi-infinite matrix such that$\sum_{i,j=1}^{+\infty}|e_{i,j}|$ is finite. We prove that the class of CQTmatrices is a Banach algebra with a suitable sub-multiplicative matrix norm$\|\cdot\|$. We introduce a finite representation of CQT matrices together withalgorithms which implement elementary matrix operations. An application tosolving quadratic matrix equations of the kind $AX^2+BX+C=0$, encountered inthe solution of Quasi-Birth and Death (QBD) stochastic processes with adenumerable set of phases, is presented where $A,B,C$ are CQT matrices.

Semi-Infinite Quasi-Toeplitz Matrices with Applications to QBD Stochastic Processes