Unconditional convergence of eigenfunction expansions for abstract and elliptic operators

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Unconditional convergence of eigenfunction expansions for abstract and elliptic operators

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

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

Name of the periodical

Proceedings of the Royal Society of Edinburgh. A - Mathematics

ISSN

0308-2105

e-ISSN

1473-7124

Volume of the periodical

155

Issue of the periodical within the volume

6

Country of publishing house

GB - UNITED KINGDOM

Number of pages

19

Pages from-to

2345-2363

UT code for WoS article

001197601700001

EID of the result in the Scopus database

2-s2.0-85190617010