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This paper extends Yosida's mean ergodic theorem in order to compute projections onto non-unitary eigenspaces for spectral operators of scalar-type on locally convex linear topological spaces.
Y Susuki and Igor Mezić, Nonlinear Koopman Modes and Coherency Identification of Coupled Swing Dynamics , Power Systems, IEEE Transactions on 26
1904
Earlier work this paper cites.
B O Koopman, Hamiltonian Systems and Transformations in Hilbert Space , Proceedings of the National Academy of Sciences of the United States of America 17
1931
Earlier work this paper cites.
N Wiener and A Wintner, Harmonic Analysis and Ergodic Theory , American Journal of Mathematics 63
1941
Earlier work this paper cites.
Nelson Dunford, Spectral Operators , Pacific Journal of Mathematics (1954), 321–354 (English)
1954
Earlier work this paper cites.
Nelson Dunford and Jacob T Schwartz, Linear Operators. Part I: General Theory , Pure and Applied Mathematics, vol. VII, Interscience Publishers, 1958 (English)
1958
Earlier work this paper cites.
Helmut H Schaefer, Spectral measures in locally convex algebras , Acta Mathematica 107
1962
Earlier work this paper cites.
Bertram Walsh, Structure of Spectral Measures on Locally Convex Spaces , Transactions of the American Mathematical Society 120
1965
Earlier work this paper cites.
William C Ridge, Spectrum of a Composition Operator , Proceedings of the American Mathematical Society 37
1973
Earlier work this paper cites.
Kosaku Yosida, Functional analysis , fifth ed., Springer-Verlag, Berlin, 1978
1978
Earlier work this paper cites.
Vladimir Igorevich Arnol d and Mark Levi, Geometrical methods in the theory of ordinary differential equations , vol. 372, Springer-Verlag New York, 1988
1988
Earlier work this paper cites.
V Rokhlin, A Fast Algorithm for the Discrete Laplace Transformation , Journal of Complexity (1988), 12–32 (English)
1988
Earlier work this paper cites.
P Wojtaszczyk, Banach Spaces for Analysts , Cambridge University Press, 1991
1991
Earlier work this paper cites.
John Strain, A fast Laplace transform based on Laguerre functions , Mathematics of Computation 58
1992
Earlier work this paper cites.
R K Singh and J S Manhas, Composition operators on Function Spaces , Mathematics Studies, Elsevier, Noth-Holland, 1993
1993
Earlier work this paper cites.
C C Cowen and B D MacCluer, Spectra of Some Composition Operators , Journal of Functional Analysis 125
1994
Cited alongside, same era.
R Lange and B Nagy, Semigroups and Scalar-Type Operators in Banach Spaces , Journal of Functional Analysis 119
1994
Cited alongside, same era.
A B Katok and Boris Hasselblatt, Introduction to the Modern Theory of Dynamical Systems , Encyclopedia of Mathematics and its Applications, Cambridge University Press, 1997 (English)
1997
Cited alongside, same era.
Lloyd N Trefethen and III David Bau, Numerical Linear Algebra , Society for Industrial and Applied Mathematics, June 1997 (English)
1997
Cited alongside, same era.
George Bachman and Lawrence Narici, Functional Analysis , reprint of 1966 edition ed., Dover Publications, New York, 2000
2000
Cited alongside, same era.
Yueheng Lan and Igor Mezić, The spectrum of Koopman operators based on linearization , Preprint (2011), 1–16
2011
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Y Saad, Numerical Methods for Large Eigenvalue Problems , 2 ed., Society for Industrial and Applied Mathematics (SIAM), 2011 (English)
2011
Later among the works it cites.
PJ Schmid, L Li, MP Juniper, and O. Pust, Applications of the dynamic mode decomposition , Theoretical and Computational Fluid Dynamics 25
2011
Later among the works it cites.
Abu Seena and Hyung Jin Sung, Dynamic mode decomposition of turbulent cavity flows for self-sustained oscillations , International Journal of Heat and Fluid Flow 32
2011
Later among the works it cites.
Marko Budisic, Ryan Mohr, and Igor Mezić, Applied Koopmanism , Chaos 22
2012
Later among the works it cites.
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Idris Assani, Wiener Wintner ergodic theorems , World Scientific Publishing Co. Inc., 2003
2003
Cited alongside, same era.
R Aron and M Lindström, Spectra of weighted composition operators on weighted banach spaces of analytic functions , Israel Journal of Mathematics 141
2004
Cited alongside, same era.
Igor Mezić, Spectral Properties of Dynamical Systems, Model Reduction and Decompositions , Nonlinear Dynamics 41
2005
Cited alongside, same era.
Peter J Schmid and J Sesterhenn, Dynamic Mode Decomposition of Numerical and Experimental Data , Sixty-First Annual Meeting of the APS Division of Fluid Dynamics (San Antonio, Texas, USA), 2008
2008
Cited alongside, same era.
P Galindo, T W Gamelin, and Mikael Lindström, Spectra of composition operators on algebras of analytic functions on Banach spaces , Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 139
2009
Cited alongside, same era.
Clarence W Rowley, Igor Mezić, Shervin Bagheri, Philipp Schlatter, and Dan S Henningson, Spectral analysis of nonlinear flows , Journal of Fluid Mechanics 641
2009
Cited alongside, same era.
Bryan Eisenhower, Tobias Maile, Martin Fischer, and Igor Mezić, Decomposing Building System Data for Model Validation and Analysis Using the Koopman Operator , SimBuild 2010 - Fourth National Conference of IBPSA-USA (2010), 8
2010
Cited alongside, same era.
Michael Georgescu, Bryan Eisenhower, and Igor Mezić, Creating zoning approximations to building energy models using the Koopman Operator , SimBuild 2012 (2012), 9
2012
Later among the works it cites.
A Mauroy and Igor Mezić, On the use of Fourier averages to compute the global isochrons of (quasi)periodic dynamics , Chaos 22
2012
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by same author, Nonlinear Koopman modes and a precursor to power system swing instabilities , Power Systems, IEEE Transactions on 27
2012
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Fredrik Andersson, Algorithms for unequally spaced fast Laplace transforms , Applied and Computational Harmonic Analysis 35
2013
Later among the works it cites.
Olli Hyvärinen, Mikael Lindström, Ilmari Nieminen, and Erno Saukko, Spectra of weighted composition operators with automorphic symbols , Journal of Functional Analysis 265
2013
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by same author, Linearization in the large of nonlinear systems and Koopman operator spectrum , Physica D: Nonlinear Phenomena 242
2013
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A Mauroy, Igor Mezić, and J Moehlis, Isostables, isochrons, and Koopman spectrum for the action-angle representation of stable fixed point dynamics , Physica D: Nonlinear Phenomena (2013), 1–37
2013
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by same author, Analysis of Fluid Flows via Spectral Properties of the Koopman Operator , Annual Review of Fluid Mechanics 45
2013
Later among the works it cites.