Expository Lecture s from th e CBMS Regional Conferenc e held a t Lincoln , Nebrask a August 198 5 Research supporte d i n par t b y Nationa l Scienc e Foundatio n Gran t DMS-83 - 01394 and Offic e o f Nava l Researc h N00014-85-K-0070 . 1980 Mathematics Subject Classifications (1985 Revision). Primar y 47-01, 46-01, 93-XX, 22-XX , 30-XX , 42-XX, 49-XX . Library of Congress Cataloging-in-Publication Dat a Helton, J. William, 1944 - Operator theory , analyti c functions, matrices , and electrica l engineering . (Regional conferenc e serie s in mathematics, ISS N 0160-7642 no. 68 ) Bibliography p . 1. Functional analysis . 2 . Operator theory . 3 . Matrices. I . Conferenc e Board of the Mathematica l Sciences . II . Title. III . Series. QA1.R33 no . 68 [QA321 ] 51 0 s [515.7] 87-119 2 ISBN 0-8218-0718- 8 Copying an d reprinting . Individua l reader s o f thi s publication , an d nonprofi t librarie s actin g fo r them, ar e permitte d t o mak e fai r us e o f th e material , suc h a s t o cop y a n articl e fo r us e i n leachin g o r research. Permissio n i s granted t o quot e brie f passage s fro m thi s publicatio n i n reviews , provide d th e customary acknowledgmen t o f the source i s given. Republication, systemati c copying, or multipl e reproductio n o f any material i n this publication (in - cluding abstracts) i s permitted onl y under license from th e American Mathematica l Society . Request s fo r such permission should be addressed t o the Executive Director, American Mathematica l Society, P.O. Box 6248, Providence , Rhod e Islan d 02940-6248. The owner consents to copying beyond tha t permitte d b y Sections 10 7 or 10 8 of the U.S. Copyright Law, provide d tha t a fe e o f $1.0 0 plu s $.2 5 pe r pag e fo r eac h cop y b e pai d directl y t o th e Copyrigh t Clearance Center , Inc. . 2 7 Congres s Street . Salem , Massachusett s 01970 . Whe n payin g thi s fe e pleas e use the cod e 0160-7642/9 0 t o refe r t o thi s publication . Thi s consen t doe s no t exten d t o othe r kind s of copying, suc h a s copyin g fo r genera l distribution , fo r advertisin g o r promotiona l purposes , fo r creatin g new collective works , or fo r resale . Copyright ©198 7 b y the American Mathematica l Society . Al l rights reserved . Printed i n the United State s of Americ a The American Mathematica l Societ y retain s all rights except thos e granted t o the Unite d State s Government . The pape r use d i n thi s book i s acid-free an d fall s withi n th e guidelines established t o ensure permanenc e an d durability . © 109 8 7 6 5 4 3 2 9 5 94 93 92 91 90
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