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03435aam a2200397 i 4500 001 4D840C0CCD6211EE9507C16149ECA4DB 003 SILO 005 20240217010049 008 221130s2023 si a b 001 0 eng 010 $a 2022051320 020 $a 9811265518 020 $a 9789811265518 035 $a (OCoLC)1361694097 040 $a DLC $b eng $e rda $c DLC $d OCLCF $d YDX $d UIU $d OCLCO $d NUI $d SILO 042 $a pcc 050 00 $a QA402 $b .J67 2023 082 00 $a 511/.5 $2 23/eng20230117 100 1 $a Jørgensen, Palle E. T., $d 1947- $e author. 245 10 $a Operator theory and analysis of infinite networks : $b theory and applications / $c Palle ET Jorgensen (University of Iowa, USA), Erin PJ Pearse (California Polytechnic State University, USA). 264 1 $a Singapore ; $b World Scientific Publishing Co. Pte. Ltd., $c [2023] 300 $a lv, 392 pages : $b illustrations ; $c 24 cm. 490 1 $a Contemporary mathematics and its applications: monographs, expositions and lecture notes, $x 2591-7668 ; $v vol. 7 520 $a "This volume considers resistance networks: large graphs which are connected, undirected, and weighted. Such networks provide a discrete model for physical processes in inhomogeneous media, including heat flow through perforated or porous media. These graphs also arise in data science, e.g., considering geometrizations of datasets, statistical inference, or the propagation of memes through social networks. Indeed, network analysis plays a crucial role in many other areas of data science and engineering. In these models, the weights on the edges may be understood as conductances, or as a measure of similarity. Resistance networks also arise in probability, as they correspond to a broad class of Markov chains. The present volume takes the nonstandard approach of analyzing resistance networks from the point of view of Hilbert space theory, where the inner product is defined in terms of Dirichlet energy. The resulting viewpoint emphasizes orthogonality over convexity and provides new insights into the connections between harmonic functions, operators, and boundary theory. Novel applications to mathematical physics are given, especially in regard to the question of self-adjointness of unbounded operators. New topics are covered in a host of areas accessible to multiple audiences, at both beginning and more advanced levels. This is accomplished by directly linking diverse applied questions to such key areas of mathematics as functional analysis, operator theory, harmonic analysis, optimization, approximation theory, and probability theory"-- $c Provided by publisher. 504 $a Includes bibliographical references and index. 650 0 $a System analysis. 650 0 $a Operator theory. 650 0 $a Hilbert space. 650 7 $a Hilbert space $2 fast $0 (OCoLC)fst00956785 650 7 $a Operator theory $2 fast $0 (OCoLC)fst01046419 650 7 $a System analysis $2 fast $0 (OCoLC)fst01141385 776 08 $i Electronic version: $a Jørgensen, Palle E. T., 1947- $t Operator theory and analysis of infinite networks. $d New Jersey : World Scientific, [2023] $z 9789811265525 $w (OCoLC)1376752156 700 1 $a Pearse, Erin P. J., $d 1975- $e author. 830 0 $a Contemporary mathematics and its applications: monographs, expositions and lecture notes ; $v v. 7. 941 $a 1 952 $l OVUX522 $d 20240217010707.0 956 $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=4D840C0CCD6211EE9507C16149ECA4DBInitiate Another SILO Locator Search