Analysis of the essential spectrum of singular matrix differential operators

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F16%3A00459128" target="_blank" >RIV/61389005:_____/16:00459128 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jde.2015.10.050" target="_blank" >http://dx.doi.org/10.1016/j.jde.2015.10.050</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jde.2015.10.050" target="_blank" >10.1016/j.jde.2015.10.050</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Analysis of the essential spectrum of singular matrix differential operators

Popis výsledku v původním jazyce

A complete analysis of the essential spectrum of matrix-differential operators A of the form (-d/dt p d/dt + q -d/dt b* + c*) b d/dt + c D) in L2((alpha, beta)) circle times (L-2((alpha, beta)))(n) singular at beta is an element of R boolean OR {infinity} is given; the coefficient functions p, q are scalar real-valued with p > 0, b, c are vector-valued, and D is Hermitian matrix-valued. The so-called "singular part of the essential spectrum" sigma(s)(ess)(A) is investigated systematically. Our main results include an explicit description of sigma(s)(ess)(A), criteria for its absence and presence; an analysis of its topological structure and of the essential spectral radius. Our key tools are: the asymptotics of the leading coefficient pi(center dot, lambda) = p - b* (D - lambda)(-1) b of the first Schur complement of (0.1), a scalar differential operator but non-linear in lambda; the Nevanlinna behaviour in lambda of certain limits t NE arrow beta of functions formed out of the coefficients in (0.1). The efficacy of our results is demonstrated by several applications; in particular, we prove a conjecture on the essential spectrum of some symmetric stellar equilibrium models.

Název v anglickém jazyce

Analysis of the essential spectrum of singular matrix differential operators

Popis výsledku anglicky

A complete analysis of the essential spectrum of matrix-differential operators A of the form (-d/dt p d/dt + q -d/dt b* + c*) b d/dt + c D) in L2((alpha, beta)) circle times (L-2((alpha, beta)))(n) singular at beta is an element of R boolean OR {infinity} is given; the coefficient functions p, q are scalar real-valued with p > 0, b, c are vector-valued, and D is Hermitian matrix-valued. The so-called "singular part of the essential spectrum" sigma(s)(ess)(A) is investigated systematically. Our main results include an explicit description of sigma(s)(ess)(A), criteria for its absence and presence; an analysis of its topological structure and of the essential spectral radius. Our key tools are: the asymptotics of the leading coefficient pi(center dot, lambda) = p - b* (D - lambda)(-1) b of the first Schur complement of (0.1), a scalar differential operator but non-linear in lambda; the Nevanlinna behaviour in lambda of certain limits t NE arrow beta of functions formed out of the coefficients in (0.1). The efficacy of our results is demonstrated by several applications; in particular, we prove a conjecture on the essential spectrum of some symmetric stellar equilibrium models.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BE - Teoretická fyzika

OECD FORD obor

—

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Differential Equations

ISSN

0022-0396

e-ISSN

—

Svazek periodika

260

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

46

Strana od-do

3881-3926

Kód UT WoS článku

000373536700024

EID výsledku v databázi Scopus

2-s2.0-84947998771