Identities for sums of characteristic values of entire matrix pencils

M. I. Gil'

doi:10.1016/j.laa.2007.08.012

Identities for sums of characteristic values of entire matrix pencils

M. I. Gil'

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The paper deals with an entire matrix-valued function of a complex argument (an entire matrix pencil) f of order ρ (f) < ∞. Identities for the following sums of the characteristic values z_k (f) (k = 1, 2, ...) of f are established:underover(∑, k = 1, ∞) frac(1, z_k^m (f)) (m > ρ (f))andunderover(∑, k = 1, ∞) fenced(Im frac(1, z_k (f)))² (ρ (f) < 2) .The suggested results are new even for polynomial pencils.

Original language	English
Pages (from-to)	814-823
Number of pages	10
Journal	Linear Algebra and Its Applications
Volume	428
Issue number	4
DOIs	https://doi.org/10.1016/j.laa.2007.08.012
State	Published - 1 Feb 2008

Keywords

Characteristic values
Entire matrix pencils

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

Access to Document

10.1016/j.laa.2007.08.012

Cite this

@article{ea18a6b1102946e68b053c93eaeff2ab,

title = "Identities for sums of characteristic values of entire matrix pencils",

abstract = "The paper deals with an entire matrix-valued function of a complex argument (an entire matrix pencil) f of order ρ (f) < ∞. Identities for the following sums of the characteristic values zk (f) (k = 1, 2, ...) of f are established:underover(∑, k = 1, ∞) frac(1, zkm (f)) (m > ρ (f))andunderover(∑, k = 1, ∞) fenced(Im frac(1, zk (f)))2 (ρ (f) < 2) .The suggested results are new even for polynomial pencils.",

keywords = "Characteristic values, Entire matrix pencils",

author = "Gil', {M. I.}",

note = "Funding Information: This research was supported by the Kamea Fund of the Israel. E-mail address: [email protected] 0024-3795/$ - see front matter ( 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.laa.2007.08.012",

year = "2008",

month = feb,

day = "1",

doi = "10.1016/j.laa.2007.08.012",

language = "English",

volume = "428",

pages = "814--823",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

number = "4",

}

TY - JOUR

T1 - Identities for sums of characteristic values of entire matrix pencils

AU - Gil', M. I.

N1 - Funding Information: This research was supported by the Kamea Fund of the Israel. E-mail address: [email protected] 0024-3795/$ - see front matter ( 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.laa.2007.08.012

PY - 2008/2/1

Y1 - 2008/2/1

N2 - The paper deals with an entire matrix-valued function of a complex argument (an entire matrix pencil) f of order ρ (f) < ∞. Identities for the following sums of the characteristic values zk (f) (k = 1, 2, ...) of f are established:underover(∑, k = 1, ∞) frac(1, zkm (f)) (m > ρ (f))andunderover(∑, k = 1, ∞) fenced(Im frac(1, zk (f)))2 (ρ (f) < 2) .The suggested results are new even for polynomial pencils.

AB - The paper deals with an entire matrix-valued function of a complex argument (an entire matrix pencil) f of order ρ (f) < ∞. Identities for the following sums of the characteristic values zk (f) (k = 1, 2, ...) of f are established:underover(∑, k = 1, ∞) frac(1, zkm (f)) (m > ρ (f))andunderover(∑, k = 1, ∞) fenced(Im frac(1, zk (f)))2 (ρ (f) < 2) .The suggested results are new even for polynomial pencils.

KW - Characteristic values

KW - Entire matrix pencils

UR - http://www.scopus.com/inward/record.url?scp=37249017469&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2007.08.012

DO - 10.1016/j.laa.2007.08.012

M3 - Article

AN - SCOPUS:37249017469

SN - 0024-3795

VL - 428

SP - 814

EP - 823

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 4

ER -

Identities for sums of characteristic values of entire matrix pencils

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this