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VOL. 33 | 1994 Indefinite integrals of functions from $L^p(\mathbb{R})$
Bolis Basit, Alan J. Pryde

Editor(s) Gaven Marten, Bevan Thompson

Abstract

In this paper we seek conditions under which the indefinite integrals of a function $\varphi$ from $L^p(\mathbb{R})$ belong to $L^p(\mathbb{R}) + \mathbb{C}$. We prove that if the spectrum sp($\varphi$) of $\varphi$ is isolated from zero, then it is improperly integrable for $(1 \leq p \lt \infty)$ and its indefinite integrals belong to $L^p(\mathbb{R}) + \mathbb{C}$. Also, we give applications to the differential equation $u^1(x) + \lambda u(x) = \varphi(x)$.

Information

Published: 1 January 1994
First available in Project Euclid: 18 November 2014

zbMATH: 0841.43013
MathSciNet: MR1332499

Rights: Copyright © 1994, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.

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