Around a multivariate Schmidt–Spitzer theorem.
Saved in:
| Title: | Around a multivariate Schmidt–Spitzer theorem. |
|---|---|
| Authors: | Alexandersson, Per1 per@math.su.se, Shapiro, Boris1 shapiro@math.su.se |
| Source: | Linear Algebra & its Applications. Apr2014, Vol. 446, p356-368. 13p. |
| Subjects: | Multivariate analysis, Arbitrary constants, Mathematical proofs, Toeplitz matrices, Polynomials |
| Abstract: | Abstract: Given an arbitrary complex-valued infinite matrix , ; and a positive integer n we introduce a naturally associated polynomial basis of . We discuss some properties of the locus of common zeros of all polynomials in having a given degree m; the latter locus can be interpreted as the spectrum of the -submatrix of formed by its m first rows and by the first columns. We initiate the study of the asymptotic of these spectra when in the case when is a banded Toeplitz matrix. In particular, we present and partially prove a conjectural multivariate analog of the well-known Schmidt–Spitzer theorem which describes the spectral asymptotic for the sequence of principal minors of an arbitrary banded Toeplitz matrix. Finally, we discuss relations between polynomial bases and multivariate orthogonal polynomials. [Copyright &y& Elsevier] |
| Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 94310580 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Around a multivariate Schmidt–Spitzer theorem. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Alexandersson%2C+Per%22">Alexandersson, Per</searchLink><relatesTo>1</relatesTo><i> per@math.su.se</i><br /><searchLink fieldCode="AR" term="%22Shapiro%2C+Boris%22">Shapiro, Boris</searchLink><relatesTo>1</relatesTo><i> shapiro@math.su.se</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Linear+Algebra+%26+its+Applications%22">Linear Algebra & its Applications</searchLink>. Apr2014, Vol. 446, p356-368. 13p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Multivariate+analysis%22">Multivariate analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Arbitrary+constants%22">Arbitrary constants</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+proofs%22">Mathematical proofs</searchLink><br /><searchLink fieldCode="DE" term="%22Toeplitz+matrices%22">Toeplitz matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Abstract: Given an arbitrary complex-valued infinite matrix , ; and a positive integer n we introduce a naturally associated polynomial basis of . We discuss some properties of the locus of common zeros of all polynomials in having a given degree m; the latter locus can be interpreted as the spectrum of the -submatrix of formed by its m first rows and by the first columns. We initiate the study of the asymptotic of these spectra when in the case when is a banded Toeplitz matrix. In particular, we present and partially prove a conjectural multivariate analog of the well-known Schmidt–Spitzer theorem which describes the spectral asymptotic for the sequence of principal minors of an arbitrary banded Toeplitz matrix. Finally, we discuss relations between polynomial bases and multivariate orthogonal polynomials. [Copyright &y& Elsevier] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Linear Algebra & its Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=94310580 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.laa.2014.01.005 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 356 Subjects: – SubjectFull: Multivariate analysis Type: general – SubjectFull: Arbitrary constants Type: general – SubjectFull: Mathematical proofs Type: general – SubjectFull: Toeplitz matrices Type: general – SubjectFull: Polynomials Type: general Titles: – TitleFull: Around a multivariate Schmidt–Spitzer theorem. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Alexandersson, Per – PersonEntity: Name: NameFull: Shapiro, Boris IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2014 Type: published Y: 2014 Identifiers: – Type: issn-print Value: 00243795 Numbering: – Type: volume Value: 446 Titles: – TitleFull: Linear Algebra & its Applications Type: main |
| ResultId | 1 |
