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Around multivariate Schmidt-Spitzer theoremPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2014 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 446, 356-368 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2014. Vol. 446, 356-368 p.
##### Keyword [en]

asymptotic root distribution, square and rectangular Toeplitz matrices
##### National Category

Mathematics
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:su:diva-88600DOI: 10.1016/j.laa.2014.01.005ISI: 000334146700024OAI: oai:DiVA.org:su-88600DiVA: diva2:612389
#####

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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt482",{id:"formSmash:j_idt482",widgetVar:"widget_formSmash_j_idt482",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt488",{id:"formSmash:j_idt488",widgetVar:"widget_formSmash_j_idt488",multiple:true});
Available from: 2013-03-21 Created: 2013-03-21 Last updated: 2017-11-22Bibliographically approved
##### In thesis

Given an arbitrary complex-valued infinite matrix $\infmatA=(a_{ij}),$$i=1,\dotsc,\infty;$ $j=1,\dotsc,\infty$ and a positive integer $n$ we introduce anaturally associated polynomial basis $\polybasis_\infmatA$ of$\C[x_0,\dotsc,x_n]$.We discuss some properties of the locus of common zeros of all polynomials in $\polybasis_A$ having a given degree $m$; the latter locus can beinterpreted as the spectrum of the $m\times (m+n)$-submatrix of $\infmatA$ formed by its $m$ first rows and$(m+n)$ first columns. We initiate the study of the asymptotics of these spectra when $m\to \infty$ inthe case when $\infmatA$ is a banded Toeplitz matrix.In particular, we present and partially prove a conjectural multivariate analogof the well-known Schmidt-Spitzer theorem which describes the spectral asymptotics for the sequence of principal minors of an arbitrarybanded Toeplitz matrix.Finally, we discuss relations between polynomial bases $\polybasis_\infmatA$ andmultivariate orthogonal polynomials.

1. Combinatorial Methods in Complex Analysis$(function(){PrimeFaces.cw("OverlayPanel","overlay613664",{id:"formSmash:j_idt762:0:j_idt766",widgetVar:"overlay613664",target:"formSmash:j_idt762:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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