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Journal articles on the topic 'Invariant subspaces – Research – Analysis'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Kuznetsov, Sergey P., and Yuliya V. Sedova. "Robust Hyperbolic Chaos in Froude Pendulum with Delayed Feedback and Periodic Braking." International Journal of Bifurcation and Chaos 29, no. 12 (November 2019): 1930035. http://dx.doi.org/10.1142/s0218127419300350.

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We indicate a possibility of implementing hyperbolic chaos using a Froude pendulum that is able to produce self-oscillations due to the suspension on a shaft rotating at constant angular velocity, in the presence of time-delay feedback and of periodic braking by the application of additional frictional force. We formulate a mathematical model and carry out its numerical research. In the parameter space we reveal areas of chaotic and regular dynamics using the analysis of Lyapunov exponents and some other diagnostic tools. It is shown that there are regions in the parameter space where the Poincaré stroboscopic map has an attractor, which is a kind of Smale–Williams solenoid embedded in the infinite-dimensional state space. We confirm the hyperbolicity of the attractor by numerical calculations including the analysis of angles of intersections of stable and unstable invariant subspaces of vectors of small perturbations for trajectories on the attractor and verify the absence of tangencies between these subspaces.

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2

Rapiejko, Piotr, Zbigniew M. Wawrzyniak, Ryszard S. Jachowicz, and Dariusz Jurkiewicz. "Image analysis in automatic system of pollen recognition." Acta Agrobotanica 59, no. 1 (2012): 385–93. http://dx.doi.org/10.5586/aa.2006.040.

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In allergology practice and research, it would be convenient to receive pollen identification and monitoring results in much shorter time than it comes from human identification. Image based analysis is one of the approaches to an automated identification scheme for pollen grain and pattern recognition on such images is widely used as a powerful tool. The goal of such attempt is to provide accurate, fast recognition and classification and counting of pollen grains by computer system for monitoring. The isolated pollen grain are objects extracted from microscopic image by CCD camera and PC computer under proper conditions for further analysis. The algorithms are based on the knowledge from feature vector analysis of estimated parameters calculated from grain characteristics, including morphological features, surface features and other applicable estimated characteristics. Segmentation algorithms specially tailored to pollen object characteristics provide exact descriptions of pollen characteristics (border and internal features) already used by human expert. The specific characteristics and its measures are statistically estimated for each object. Some low level statistics for estimated local and global measures of the features establish the feature space. Some special care should be paid on choosing these feature and on constructing the feature space to optimize the number of subspaces for higher recognition rates in low-level classification for type differentiation of pollen grains.The results of estimated parameters of feature vector in low dimension space for some typical pollen types are presented, as well as some effective and fast recognition results of performed experiments for different pollens. The findings show the ewidence of using proper chosen estimators of central and invariant moments (M21, NM2, NM3, NM8 NM9), of tailored characteristics for good enough classification measures (efficiency > 95%), even for low dimensional classifiers (≥ 3) for type differentiation of pollens grain.

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3

Beattie, Christopher, Mark Embree, and John Rossi. "Convergence of Restarted Krylov Subspaces to Invariant Subspaces." SIAM Journal on Matrix Analysis and Applications 25, no. 4 (January 2004): 1074–109. http://dx.doi.org/10.1137/s0895479801398608.

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4

Omladič, Matjaž. "Perturbation of Invariant Subspaces." Journal of Mathematical Analysis and Applications 197, no. 1 (January 1996): 125–37. http://dx.doi.org/10.1006/jmaa.1996.0011.

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5

Baranov, Anton, and Yurii Belov. "Synthesizable differentiation-invariant subspaces." Geometric and Functional Analysis 29, no. 1 (February 2019): 44–71. http://dx.doi.org/10.1007/s00039-019-00474-8.

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6

Djordjević, Slaviša V., Robin E. Harte, and David R. Larson. "Partially hyper invariant subspaces." Operators and Matrices, no. 1 (2012): 97–106. http://dx.doi.org/10.7153/oam-06-07.

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7

Apostol, Constantin, Ciprian Foias, and Norberto Salinas. "On stable invariant subspaces." Integral Equations and Operator Theory 8, no. 6 (November 1985): 721–50. http://dx.doi.org/10.1007/bf01213789.

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8

Turovskii, Yu V. "Volterra Semigroups Have Invariant Subspaces." Journal of Functional Analysis 162, no. 2 (March 1999): 313–22. http://dx.doi.org/10.1006/jfan.1998.3368.

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9

Chalendar, Isabelle, and Jonathan R. Partington. "Constrained approximation and invariant subspaces." Journal of Mathematical Analysis and Applications 280, no. 1 (April 2003): 176–87. http://dx.doi.org/10.1016/s0022-247x(03)00099-4.

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10

Kovarik, Zdislav V., and Nagwa Sherif. "Perturbation of invariant subspaces." Linear Algebra and its Applications 64 (January 1985): 93–113. http://dx.doi.org/10.1016/0024-3795(85)90269-1.

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11

Dongarra, Jack J., Sven Hammarling, and James H. Wilkinson. "Numerical Considerations in Computing Invariant Subspaces." SIAM Journal on Matrix Analysis and Applications 13, no. 1 (January 1992): 145–61. http://dx.doi.org/10.1137/0613013.

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12

McCullough, Scott, and Tavan T. Trent. "Invariant Subspaces and Nevanlinna–Pick Kernels." Journal of Functional Analysis 178, no. 1 (December 2000): 226–49. http://dx.doi.org/10.1006/jfan.2000.3664.

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13

Atzmon, Aharon. "Maximal, Minimal, and Primary Invariant Subspaces." Journal of Functional Analysis 185, no. 1 (September 2001): 155–213. http://dx.doi.org/10.1006/jfan.2001.3760.

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14

Byers, Ralph, and Daniel Kressner. "Structured Condition Numbers for Invariant Subspaces." SIAM Journal on Matrix Analysis and Applications 28, no. 2 (January 2006): 326–47. http://dx.doi.org/10.1137/050637601.

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15

Popov, Alexey I., and Adi Tcaciuc. "Every operator has almost-invariant subspaces." Journal of Functional Analysis 265, no. 2 (July 2013): 257–65. http://dx.doi.org/10.1016/j.jfa.2013.04.002.

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16

MacDonald, Gordon W. "Invariant subspaces for Bishop-type operators." Journal of Functional Analysis 91, no. 2 (July 1990): 287–311. http://dx.doi.org/10.1016/0022-1236(90)90146-c.

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17

Bercovici, Hari. "The quasisimilarity orbits of invariant subspaces." Journal of Functional Analysis 95, no. 2 (February 1991): 344–63. http://dx.doi.org/10.1016/0022-1236(91)90033-2.

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18

Ambrozie, Călin, and Vladimı́r Müller. "Invariant subspaces for polynomially bounded operators." Journal of Functional Analysis 213, no. 2 (August 2004): 321–45. http://dx.doi.org/10.1016/j.jfa.2003.12.004.

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19

Popescu, Gelu. "Characteristic functions and joint invariant subspaces." Journal of Functional Analysis 237, no. 1 (August 2006): 277–320. http://dx.doi.org/10.1016/j.jfa.2006.01.019.

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20

Kérchy, László. "Shift-type invariant subspaces of contractions." Journal of Functional Analysis 246, no. 2 (May 2007): 281–301. http://dx.doi.org/10.1016/j.jfa.2007.01.011.

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21

Kim, Yun-Su. "Algebraic elements and invariant subspaces." Operators and Matrices, no. 3 (2011): 449–54. http://dx.doi.org/10.7153/oam-05-32.

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22

Eschmeier, J�rg, and Bebe Prunaru. "Invariant subspaces and localizable spectrum." Integral Equations and Operator Theory 42, no. 4 (December 2002): 461–71. http://dx.doi.org/10.1007/bf01270923.

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23

Szekelyhidi, Laszlo, and Seyyed Mohammad Tabatabaie. "Invariant Subspaces on KPC-Hypergroups." Zurnal matematiceskoj fiziki, analiza, geometrii 15, no. 1 (March 25, 2019): 122–30. http://dx.doi.org/10.15407/mag15.01.122.

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24

Godefroy, Gilles. "Convex analysis and non-trivial invariant subspaces." Positivity 24, no. 2 (May 25, 2019): 369–72. http://dx.doi.org/10.1007/s11117-019-00682-4.

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25

Shul'man, V. S., and Yu V. Turovskii. "Joint spectral radius and invariant subspaces." Functional Analysis and Its Applications 34, no. 2 (April 2000): 156–58. http://dx.doi.org/10.1007/bf02482436.

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26

Gomilko, A. M. "Invariant subspaces of J-dissipative operators." Functional Analysis and Its Applications 19, no. 3 (1986): 213–14. http://dx.doi.org/10.1007/bf01076623.

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27

Gromov, A. L. "Invariant subspaces of weighted permutation operators." Functional Analysis and Its Applications 22, no. 2 (1988): 147–48. http://dx.doi.org/10.1007/bf01077612.

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28

Fernández-Morales, H. R., A. G. García, M. A. Hernández-Medina, and M. J. Muñoz-Bouzo. "Generalized sampling: From shift-invariant to U-invariant spaces." Analysis and Applications 13, no. 03 (March 5, 2015): 303–29. http://dx.doi.org/10.1142/s0219530514500213.

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The aim of this article is to derive a sampling theory in U-invariant subspaces of a separable Hilbert space ℋ where U denotes a unitary operator defined on ℋ. To this end, we use some special dual frames for L2(0, 1), and the fact that any U-invariant subspace with stable generator is the image of L2(0, 1) by means of a bounded invertible operator. The used mathematical technique mimics some previous sampling work for shift-invariant subspaces of L2(ℝ). Thus, sampling frame expansions in U-invariant spaces are obtained. In order to generalize convolution systems and deal with the time-jitter error in this new setting we consider a continuous group of unitary operators which includes the operator U.

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29

Dykema, K., and U. Haagerup. "Invariant subspaces of Voiculescu's circular operator." Geometric and Functional Analysis 11, no. 4 (November 2001): 693–741. http://dx.doi.org/10.1007/pl00001682.

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30

Dykema, Ken, and Uffe Haagerup. "Invariant subspaces of the quasinilpotent DT-operator." Journal of Functional Analysis 209, no. 2 (April 2004): 332–66. http://dx.doi.org/10.1016/s0022-1236(03)00167-8.

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31

Abramovich, Y. A., C. D. Aliprantis, and O. Burkinshaw. "Invariant Subspaces of Operators on lp-Spaces." Journal of Functional Analysis 115, no. 2 (August 1993): 418–24. http://dx.doi.org/10.1006/jfan.1993.1097.

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32

Cigler, Grega, Roman Drnovšek, Damjana Kokol-Bukovšek, Matjaž Omladič, Thomas J. Laffey, Heydar Radjavi, and Peter Rosenthal. "Invariant Subspaces for Semigroups of Algebraic Operators." Journal of Functional Analysis 160, no. 2 (December 1998): 452–65. http://dx.doi.org/10.1006/jfan.1998.3293.

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33

El-Fallah, O., Y. Elmadani, and K. Kellay. "Cyclicity and invariant subspaces in Dirichlet spaces." Journal of Functional Analysis 270, no. 9 (May 2016): 3262–79. http://dx.doi.org/10.1016/j.jfa.2016.02.027.

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34

Rudin, Walter. "Invariant subspaces of H2 on a torus." Journal of Functional Analysis 61, no. 3 (May 1985): 378–84. http://dx.doi.org/10.1016/0022-1236(85)90029-1.

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35

Froelich, John. "Compact operators, invariant subspaces, and spectral synthesis." Journal of Functional Analysis 81, no. 1 (November 1988): 1–37. http://dx.doi.org/10.1016/0022-1236(88)90110-3.

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36

Gracia, Juan-Miguel, and Francisco E. Velasco. "Stability of controlled invariant subspaces." Linear Algebra and its Applications 418, no. 2-3 (October 2006): 416–34. http://dx.doi.org/10.1016/j.laa.2006.02.021.

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37

Radkova, D., and A. J. van zanten. "Constacyclic codes as invariant subspaces." Linear Algebra and its Applications 430, no. 2-3 (January 2009): 855–64. http://dx.doi.org/10.1016/j.laa.2008.09.036.

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38

Prunaru, Bebe. "K-spectral sets and invariant subspaces." Integral Equations and Operator Theory 26, no. 3 (September 1996): 367–70. http://dx.doi.org/10.1007/bf01306549.

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39

Atzmon, A., G. Godefroy, and N. J. Kalton. "Invariant Subspaces and the Exponential Map." Positivity 8, no. 2 (June 2004): 101–7. http://dx.doi.org/10.1023/b:post.0000042837.92132.73.

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40

Chattopadhyay, Arup, B. Krishna Das, and Jaydeb Sarkar. "Inner multipliers and Rudin type invariant subspaces." Acta Scientiarum Mathematicarum 82, no. 34 (2016): 519–28. http://dx.doi.org/10.14232/actasm-015-773-y.

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41

Otsuka, Naohisa, and Haruo Hinata. "Generalized Invariant Subspaces for Infinite-Dimensional Systems." Journal of Mathematical Analysis and Applications 252, no. 1 (December 2000): 325–41. http://dx.doi.org/10.1006/jmaa.2000.7011.

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42

Barria, J. "On Invariant Subspaces for Rational Toeplitz Operators." Journal of Mathematical Analysis and Applications 192, no. 1 (May 1995): 220–29. http://dx.doi.org/10.1006/jmaa.1995.1168.

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43

Ji, Guoxing. "Subdiagonal algebras with Beurling type invariant subspaces." Journal of Mathematical Analysis and Applications 480, no. 2 (December 2019): 123409. http://dx.doi.org/10.1016/j.jmaa.2019.123409.

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44

Androulakis, George. "A new method for constructing invariant subspaces." Journal of Mathematical Analysis and Applications 333, no. 2 (September 2007): 1254–63. http://dx.doi.org/10.1016/j.jmaa.2006.12.023.

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45

Mastnak, Mitja, Matjaž Omladič, and Heydar Radjavi. "Near-invariant subspaces for matrix groups are nearly invariant." Linear Algebra and its Applications 505 (September 2016): 269–81. http://dx.doi.org/10.1016/j.laa.2016.05.005.

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46

Akeroyd, John R., Dmitry Khavinson, and Harold S. Shapiro. "Weak compactness in certain star-shift invariant subspaces." Journal of Functional Analysis 202, no. 1 (August 2003): 98–122. http://dx.doi.org/10.1016/s0022-1236(03)00060-0.

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47

Freiling, Gerhard, Volker Mehrmann, and Hongguo Xu. "Existence, Uniqueness, and Parametrization of Lagrangian Invariant Subspaces." SIAM Journal on Matrix Analysis and Applications 23, no. 4 (January 2002): 1045–69. http://dx.doi.org/10.1137/s0895479800377228.

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48

Korenblum, B., and M. Stessin. "On Toeplitz-Invariant Subspaces of the Bergman Space." Journal of Functional Analysis 111, no. 1 (January 1993): 76–96. http://dx.doi.org/10.1006/jfan.1993.1005.

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49

Hernandez, Francisco L., and Evgueni M. Semenov. "Subspaces Generated by Translations in Rearrangement Invariant Spaces." Journal of Functional Analysis 169, no. 1 (December 1999): 52–80. http://dx.doi.org/10.1006/jfan.1999.3493.

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50

Patel, R. V., Z. Lin, and P. Misra. "Computation of Stable Invariant Subspaces of Hamiltonian Matrices." SIAM Journal on Matrix Analysis and Applications 15, no. 1 (January 1994): 284–98. http://dx.doi.org/10.1137/s0895479889171352.

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