Unconditional convergence of eigenfunction expansions for abstract and elliptic operators

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00642962" target="_blank" >RIV/67985840:_____/25:00642962 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1017/prm.2024.40" target="_blank" >https://doi.org/10.1017/prm.2024.40</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1017/prm.2024.40" target="_blank" >10.1017/prm.2024.40</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Unconditional convergence of eigenfunction expansions for abstract and elliptic operators

Popis výsledku v původním jazyce

We study the most general class of eigenfunction expansions for abstract normal operators with pure point spectrum in a complex Hilbert space. We find sufficient conditions for such expansions to be unconditionally convergent in spaces with two norms and also estimate the degree of this convergence. Our result essentially generalizes and complements the known theorems of Krein and of Krasnosel’skiı̆ and Pustyl’nik. We apply it to normal elliptic pseudodifferential operators on compact boundaryless C∞-manifolds. We find generic conditions for eigenfunction expansions induced by such operators to converge unconditionally in the Sobolev spaces Wpℓ with p > 2 or in the spaces Cℓ (specifically, for the p-th mean or uniform convergence on the manifold). These conditions are sufficient and necessary for the indicated convergence on Sobolev or Hörmander function classes and are given in terms of parameters characterizing these classes. We also find estimates for the degree of the convergence on such function classes. These results are new even for differential operators on the circle and for multiple Fourier series.

Název v anglickém jazyce

Unconditional convergence of eigenfunction expansions for abstract and elliptic operators

Popis výsledku anglicky

We study the most general class of eigenfunction expansions for abstract normal operators with pure point spectrum in a complex Hilbert space. We find sufficient conditions for such expansions to be unconditionally convergent in spaces with two norms and also estimate the degree of this convergence. Our result essentially generalizes and complements the known theorems of Krein and of Krasnosel’skiı̆ and Pustyl’nik. We apply it to normal elliptic pseudodifferential operators on compact boundaryless C∞-manifolds. We find generic conditions for eigenfunction expansions induced by such operators to converge unconditionally in the Sobolev spaces Wpℓ with p > 2 or in the spaces Cℓ (specifically, for the p-th mean or uniform convergence on the manifold). These conditions are sufficient and necessary for the indicated convergence on Sobolev or Hörmander function classes and are given in terms of parameters characterizing these classes. We also find estimates for the degree of the convergence on such function classes. These results are new even for differential operators on the circle and for multiple Fourier series.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Proceedings of the Royal Society of Edinburgh. A - Mathematics

ISSN

0308-2105

e-ISSN

1473-7124

Svazek periodika

155

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

19

Strana od-do

2345-2363

Kód UT WoS článku

001197601700001

EID výsledku v databázi Scopus

2-s2.0-85190617010