{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T07:54:07Z","timestamp":1787385247606,"version":"build-2736575974"},"reference-count":63,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p>In this paper, we present conditions that ensure the existence of Bochner integrable solutions of infinite dimensional Riccati integral equations. In particular, we focus on $\\mathscr{I}_p$-valued continuous solutions. We formulate an optimal sensor location problem that is based on optimal filtering and show that when the underlying system is of convection-diffusion type the Riccati integral equation has Bochner integrable solutions. We use these results to approximate the sensor placement problem by using a simple quadrature rule. A numerical example is given to illustrate the results.<\/jats:p>","DOI":"10.1137\/130948513","type":"journal-article","created":{"date-parts":[[2015,9,8]],"date-time":"2015-09-08T11:53:52Z","timestamp":1441713232000},"page":"2846-2877","source":"Crossref","is-referenced-by-count":20,"title":["Solutions and Approximations to the Riccati Integral Equation with Values in a Space of Compact Operators"],"prefix":"10.1137","volume":"53","author":[{"given":"John A.","family":"Burns","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Carlos N.","family":"Rautenberg","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2015,9,8]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"W. Arendt, C. J. K. Batty, M. Hieber, and F. 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