A Hilbert Space Stability Theory over Locally Compact Abelian Groups

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Previous article Next article A Hilbert Space Stability Theory over Locally Compact Abelian GroupsM. I. Freedman, P. L. Falb, and G. ZamesM. I. Freedman, P. L. Falb, and G. Zameshttps://doi.org/10.1137/0307035PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] P. L. Falb and , M. I. Freedman, A generalized transform theory for causal operators, SIAM J. Control, 7 (1969), 452–471 10.1137/0307033 MR0682782 0185.21403 LinkISIGoogle Scholar[2] G. Zames, On the input-output stability of time-varying nonlinear feedback systems. I, II, IEEE Trans. Automatic Control, AC-11 (1966), 228–238, 465–476 Google Scholar[3] N. Dunford and , J. Schwartz, Linear Operators. Part I: General Theory, Interscience, New York, 1958 0084.10402 Google Scholar[4] Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley and Sons), New York-London, 1962ix+285 MR0152834 0107.09603 Google Scholar[5] Frigyes Riesz and , Béla Sz.-Nagy, Functional analysis, Frederick Ungar Publishing Co., New York, 1955xii+468 MR0071727 Google Scholar[6] P. R. Halmos, Introduction to Hilbert Space and the theory of Spectral Multiplicity, Chelsea Publishing Company, New York, N. Y., 1951, 114– MR0045309 0045.05702 Google Scholar[7] M. Naimark, Normed Rings, P. Noordhoff, Groningen, Netherlands, 1959 0089.10102 Google Scholar[8] Lynn H. Loomis, An introduction to abstract harmonic analysis, D. Van Nostrand Company, Inc., Toronto-New York-London, 1953x+190, Van Nostrand, Princeton MR0054173 0052.11701 Google Scholar[9] G. Zames and , P. L. Falb, Stability conditions for systems with monotone and slope-restricted nonlinearities, SIAM J. Control, 6 (1968), 89–108 10.1137/0306007 MR0229470 0157.15801 LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Stability, Extended Spaces and Numerical RangesD. J. Allwright and A. I. Mees17 February 2012 | SIAM Journal on Control and Optimization, Vol. 20, No. 3AbstractPDF (1169 KB)Feedback Systems Described by Monotone OperatorsVaclav Dolezal18 July 2006 | SIAM Journal on Control and Optimization, Vol. 17, No. 3AbstractPDF (2157 KB)Stability Criteria for Time-Varying Systems in Hilbert SpaceAndrew Acker18 July 2006 | SIAM Journal on Control, Vol. 13, No. 6AbstractPDF (1644 KB)Circle Criteria for Stability in Hilbert SpaceP. A. Cook18 July 2006 | SIAM Journal on Control, Vol. 13, No. 3AbstractPDF (1207 KB)A Generalized Transform Theory for Causal OperatorsP. L. Falb and M. I. Freedman18 July 2006 | SIAM Journal on Control, Vol. 7, No. 3AbstractPDF (1784 KB)A Note on Causality and AnalyticityM. I. Freedman, P. L. Falb, and J. Anton18 July 2006 | SIAM Journal on Control, Vol. 7, No. 3AbstractPDF (609 KB) Volume 7, Issue 3| 1969SIAM Journal on Control History Submitted:13 August 1968Published online:18 July 2006 InformationCopyright © 1969 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0307035Article page range:pp. 479-495ISSN (print):0036-1402Publisher:Society for Industrial and Applied Mathematics