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• W2091617281 abstract "Next article On Helixes in Hilbert Space. IP. MasaniP. Masanihttps://doi.org/10.1137/1117001PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. L. Doob, Stochastic processes, John Wiley & Sons Inc., New York, 1953viii+654 MR0058896 0053.26802 Google Scholar[2] Paul R. Halmos, Shifts on Hilbert spaces, J. Reine Angew. Math., 208 (1961), 102–112 MR0152896 0107.09802 Google Scholar[3] Einar Hille and , Ralph S. Phillips, Functional analysis and semi-groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957xii+808 MR0089373 Google Scholar[4] Kiyosi Itô, Stationary random distributions, Mem. Coll. Sci. Univ. Kyoto. Ser. A. Math., 28 (1954), 209–223 MR0065060 0059.11505 CrossrefGoogle Scholar[5] K. Karhunen, Über lineare Methoden in der Wahrscheinlichkeitsrechnung, Ann. Acad. Sci. Fenn. Ser. Al., 37 (1967), Google Scholar[6] A. N. Kolmogorov, Curves in Hilbert space, which are invariant with respect to a one-parameter group of motions, DAN SSSR, 26 (1940), 6–9, (In Russian.) Google Scholar[7] A. N. Kolmogorov, Weiner's spiral and certain other interesting curves in Hilbert space, DAN SSSR, 26 (1940), 115–118, (In Russian.) Google Scholar[8] M. Krein, On the problem of continuation of helical arcs in Hilbert space, C. R. (Doklady) Acad. Sci. URSS (N.S.), 45 (1944), 139–142, (In Russian.) MR0012176 0063.03354 Google Scholar[9] J. K. Lee, The completeness of a class of functions in generalized harmonic analysis, Amer. Math. Soc. Notices, 17 (1970), 634–, (Abstract), 1957 Google Scholar[10] P. Masani, Isometric flows on Hilbert space, Bull Amer. Math. Soc., 68 (1962), 624–632 MR0145356 0117.34203 CrossrefGoogle Scholar[11] P. Masani, Orthogonally scattered measures, Advances in Math., 2 (1968), 61–117 (1968) 10.1016/0001-8708(68)90018-2 MR0228651 0187.38705 CrossrefGoogle Scholar[12] P. Masani, On the representation theorem of scattering, Bull. Amer. Math. Soc., 74 (1968), 618–624 MR0223933 0172.40803 CrossrefGoogle Scholar[13] P. Masani, Quasi-isometric measures and their applications, Bull. Amer. Math. Soc., 76 (1970), 427–528 MR0259062 0207.44001 CrossrefGoogle Scholar[14] P. Masani and , J. Robertson, The time-domain analysis of a continuous parameter weakly stationary stochastic process, Pacific J. Math., 12 (1962), 1361–1378 MR0149562 0113.33403 CrossrefGoogle Scholar[15] Yu. A. Rozanov, Spectral analysis of abstract functions, Theor. Probability Appl., 4 (1959), 271–287 10.1137/1104027 MR0123357 0089.32602 LinkGoogle Scholar[16] I. J. Schoenberg, Metric spaces and positive definite functions, Trans. Amer. Math. Soc., 44 (1938), 522–536 MR1501980 0019.41502 CrossrefGoogle Scholar[17] I. J. Schoenberg, Metric spaces and completely monotone functions, Ann. of Math. (2), 39 (1938), 811–841 MR1503439 0019.41503 CrossrefGoogle Scholar[18] J. von Neumann and , I. J. Schoenberg, Fourier integrals and metric geometry, Bull. Amer. Math. Soc., 42 (1936), 632–633, (Abstract) Google Scholar[19] J. von Neumann and , I. J. Schoenberg, Fourier integrals and metric geometry, Trans. Amer. Math. Soc., 50 (1941), 226–251 MR0004644 0028.41002 CrossrefGoogle Scholar[20] N. Wiener, Differential space, J. Math. Phys., 2 (1923), 131–174 Google Scholar[21] A. M. Yaglom, Correlation theory of processes with random stationary nth increments, Mat. Sb. N.S., 37(79) (1955), 141–196, (In Russian.) MR0071672 Google Scholar Next article FiguresRelatedReferencesCited ByDetails Sub-exponential convergence to equilibrium for Gaussian driven Stochastic Differential Equations with semi-contractive driftElectronic Journal of Probability, Vol. 25, No. 0 | 1 Jan 2020 Cross Ref Reflection Negative Kernels and Fractional Brownian MotionSymmetry, Vol. 10, No. 6 | 1 June 2018 Cross Ref A Classical Model for Storage System ActivityMathematical Adventures in Performance Analysis | 1 September 2014 Cross Ref Gaussian Moving Averages and SemimartingalesElectronic Journal of Probability, Vol. 13, No. none | 1 Jan 2008 Cross Ref Spirals in Hilbert space: With an application in information theoryExpositiones Mathematicae, Vol. 23, No. 1 | 1 Apr 2005 Cross Ref On Recovery of a Measure from Its SymmetrizationTheory of Probability & Its Applications, Vol. 49, No. 2 | 25 July 2006AbstractPDF (163 KB)Gaussian moving averages, semimartingales and option pricingStochastic Processes and their Applications, Vol. 109, No. 1 | 1 Jan 2004 Cross Ref Metric geometryI.J. 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Cross Ref Volume 17, Issue 1| 1972Theory of Probability & Its Applications1-198 History Submitted:24 September 1970Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1117001Article page range:pp. 1-19ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics" @default.
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