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2019 Cordial Volterra integral operators in spaces $L^{p}(0,T)$
Gennadi Vainikko
J. Integral Equations Applications 31(2): 283-305 (2019). DOI: 10.1216/JIE-2019-31-2-283

Abstract

A necessary and sufficient condition for the core function $\varphi \in L^{1}(0,1)$ is established in order to define a bounded cordial Volterra integral operator $(V_{\varphi }u)(t)=\int _{0}^{t}t^{-1}\varphi (t^{-1}s)u(s)\,ds$ in a space $L^{p}(0,T)$ for a $p\in [1,\infty ]$. This condition implies the boundedness of $V_{\varphi }$ also in the Sobolev spaces $W^{m,p}(0,T)$, $m\geq 1$. The spectra of $V_{\varphi }$ in the spaces $L^{p}(0,T)$ and $W^{m,p}(0,T)$ are determined and the spectral properties of $V_{\varphi }$ are examined in $L^{p}(0,T)$.

Citation

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Gennadi Vainikko. "Cordial Volterra integral operators in spaces $L^{p}(0,T)$." J. Integral Equations Applications 31 (2) 283 - 305, 2019. https://doi.org/10.1216/JIE-2019-31-2-283

Information

Published: 2019
First available in Project Euclid: 23 September 2019

zbMATH: 07118805
MathSciNet: MR4010588
Digital Object Identifier: 10.1216/JIE-2019-31-2-283

Subjects:
Primary: ‎45P05‎
Secondary: 45H05 , 47B38

Keywords: boundedness and spectra of cordial operators in spaces $L^{p}$ and $W^{p , Cordial Volterra integral operators , m}$

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.31 • No. 2 • 2019
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