A Note on the Krylov Solvability of Compact Normal Operators on Hilbert Space

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F23%3AA0000145" target="_blank" >RIV/47813059:19610/23:A0000145 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s11785-023-01413-0" target="_blank" >https://link.springer.com/article/10.1007/s11785-023-01413-0</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11785-023-01413-0" target="_blank" >10.1007/s11785-023-01413-0</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A Note on the Krylov Solvability of Compact Normal Operators on Hilbert Space

Popis výsledku v původním jazyce

We analyse the Krylov solvability of inverse linear problems on Hilbert space H where the underlying operator is compact and normal. Krylov solvability is an important feature of inverse linear problems that has profound implications in theoretical and applied numerical analysis as it is critical to understand the utility of Krylov based methods for solving inverse problems. Our results explicitly describe for the first time the Krylov subspace for such operators given any datum vector g is an element of H, as well as prove that all inverse linear problems are Krylov solvable provided that g is in the range of such an operator. We therefore expand our knowledge of the class of Krylov solvable operators to include the normal compact operators. We close the study by proving an isomorphism between the closed Krylov subspace for a general bounded normal operator and an L-2-measure space based on the scalar spectral measure.

Název v anglickém jazyce

A Note on the Krylov Solvability of Compact Normal Operators on Hilbert Space

Popis výsledku anglicky

We analyse the Krylov solvability of inverse linear problems on Hilbert space H where the underlying operator is compact and normal. Krylov solvability is an important feature of inverse linear problems that has profound implications in theoretical and applied numerical analysis as it is critical to understand the utility of Krylov based methods for solving inverse problems. Our results explicitly describe for the first time the Krylov subspace for such operators given any datum vector g is an element of H, as well as prove that all inverse linear problems are Krylov solvable provided that g is in the range of such an operator. We therefore expand our knowledge of the class of Krylov solvable operators to include the normal compact operators. We close the study by proving an isomorphism between the closed Krylov subspace for a general bounded normal operator and an L-2-measure space based on the scalar spectral measure.

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

2023

Kód důvěrnosti údajů

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

Název periodika

Complex Analysis and Operator Theory

ISSN

1661-8254

e-ISSN

1661-8262

Svazek periodika

17

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

12

Strana od-do

„109-1“-„109-12“

Kód UT WoS článku

001066912100001

EID výsledku v databázi Scopus

2-s2.0-85171555783