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Journal articles on the topic 'Random operators'

Author: Grafiati

Published: 4 June 2021

Last updated: 30 January 2023

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1

Pankov, Alexander A. "Fredholm random operators and random subspaces in Banach spaces." Czechoslovak Mathematical Journal 36, no. 3 (1986): 427–33. http://dx.doi.org/10.21136/cmj.1986.102103.

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2

Saadati, Reza. "Random compact operators." Filomat 30, no. 3 (2016): 515–23. http://dx.doi.org/10.2298/fil1603515s.

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Random compact operators are useful to study random differentiation and random integral equations. In this paper, we define the random norm of R-bounded operators and study random norms of differentiation operators and integral operators. The definition of random norm of R-bounded operators led us to study the random operator theory.

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3

Kirsch, Werner, Bernd Metzger, and Peter Müller. "Random Block Operators." Journal of Statistical Physics 143, no. 6 (June 2011): 1035–54. http://dx.doi.org/10.1007/s10955-011-0230-y.

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4

Astashkin, S. V., D. V. Zanin, E. M. Semenov, and F. A. Sukochev. "Kruglov operator and operators defined by random permutations." Functional Analysis and Its Applications 43, no. 2 (June 2009): 83–95. http://dx.doi.org/10.1007/s10688-009-0013-2.

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5

Gutierrez-Pavón, Jonathan, and Carlos G. Pacheco. "Inverting weak random operators." Random Operators and Stochastic Equations 27, no. 1 (March 1, 2019): 53–63. http://dx.doi.org/10.1515/rose-2019-2003.

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Abstract We analyze two weak random operators, initially motivated from processes in random environment. At first glance, these operators are ill-defined, but using bilinear forms, one can deal with them in a rigorous way. This point of view can be found, for instance, in [A. V. Skorohod, Random Linear Operators, Math. Appl. (Sov. Ser.), D. Reidel Publishing, Dordrecht, 1984], and it remarkably helps to carry out specific calculations. In this paper, we find explicitly the inverse of such weak operators by providing the closed forms of the so-called Green kernel. We show how this approach helps to analyze the spectra of the operators. In addition, we provide the existence of strong operators associated to our bilinear forms. Important tools that we use are the Sturm–Liouville theory and the stochastic calculus.

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6

del Rio, Rafael. "Random Sturm–Liouville operators." Applied Mathematics Letters 24, no. 2 (February 2011): 179–83. http://dx.doi.org/10.1016/j.aml.2010.08.041.

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7

Thang, Dang Hung, and Pham The Anh. "Random fixed points of completely random operators." Random Operators and Stochastic Equations 21, no. 1 (January 1, 2013): 1–20. http://dx.doi.org/10.1515/rose-2013-0001.

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8

Khan, Abdul Rahim, and Nawab Hussain. "Random fixed points for ∗-nonexpansive random operators." Journal of Applied Mathematics and Stochastic Analysis 14, no. 4 (January 1, 2001): 341–49. http://dx.doi.org/10.1155/s1048953301000302.

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The notion of a ∗-nonexpansive multivalued map is different from that of a continuous map. In this paper we prove some fixed point theorems for ∗-nonexpansive multivalued random operators in the setup of Banach spaces and Fréchet spaces. Our work generalizes, refines and improves the earlier results of a number of authors.

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9

Yin, Jiandong, and Zhongdong Liu. "Random Fixed Point Theorems of Random Comparable Operators and an Application." Discrete Dynamics in Nature and Society 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/426568.

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We introduce the new concept of random comparable operators as a generalization of random monotone operators and prove several random fixed point theorems for such a class of operators in partially ordered Banach spaces. Part of the presented results generalize and extend some known results of random monotone operators. Finally, as an application, we consider the existence of the solution of a random Hammerstein integral equation.

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10

Hála, Martin. "Asymptotic normality of eigenvalues of random ordinary differential operators." Applications of Mathematics 36, no. 4 (1991): 264–76. http://dx.doi.org/10.21136/am.1991.104465.

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11

Beg, Ismat, and Mujahid Abbas. "Common random fixed points of compatible random operators." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–15. http://dx.doi.org/10.1155/ijmms/2006/23486.

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We construct a random iteration scheme and study necessary conditions for its convergence to a common random fixed point of two pairs of compatible random operators satisfying Meir-Keeler type conditions in Polish spaces. Some random fixed point theorems for weakly compatible random operators under generalized contractive conditions in the framework of symmetric spaces are also proved.

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12

Breuer, Jonathan, Peter J. Forrester, and Uzy Smilansky. "Random discrete Schrödinger operators from random matrix theory." Journal of Physics A: Mathematical and Theoretical 40, no. 5 (January 17, 2007): F161—F168. http://dx.doi.org/10.1088/1751-8113/40/5/f03.

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13

Khan, A. R., and A. A. Domlo. "Random fixed points of multivalued inward random operators." Journal of Applied Mathematics and Stochastic Analysis 2006 (November 9, 2006): 1–8. http://dx.doi.org/10.1155/jamsa/2006/19428.

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The purpose of this paper is to provide a substantial improvement and random analogues of several results due to Benavides and Ramírez (2004). Our work sets random versions of the results of Shahzad and Lone (2005) and improves the work of Plubtieng and Kumam (2006).

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14

Shahzad, Naseer. "Random fixed points of pseudo-contractive random operators." Journal of Mathematical Analysis and Applications 296, no. 1 (August 2004): 302–8. http://dx.doi.org/10.1016/j.jmaa.2004.04.017.

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15

Kapica, Rafał. "Random iteration and Markov operators." Journal of Difference Equations and Applications 22, no. 2 (September 14, 2015): 295–305. http://dx.doi.org/10.1080/10236198.2015.1083017.

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16

Heinrich, Stefan. "Invertibility of random fredholm operators." Stochastic Analysis and Applications 8, no. 1 (January 1990): 1–59. http://dx.doi.org/10.1080/07362999008809197.

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17

Heller, Michael, Leszek Pysiak, and Wiesłw Sasin. "Noncommutative Dynamics of Random Operators." International Journal of Theoretical Physics 44, no. 6 (June 2005): 619–28. http://dx.doi.org/10.1007/s10773-005-3992-7.

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18

Knill, Oliver. "Renormalization of random Jacobi operators." Communications in Mathematical Physics 164, no. 1 (July 1994): 195–215. http://dx.doi.org/10.1007/bf02108812.

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19

Hamza, Eman, Alain Joye, and Günter Stolz. "Localization for Random Unitary Operators." Letters in Mathematical Physics 75, no. 3 (January 14, 2006): 255–72. http://dx.doi.org/10.1007/s11005-005-0044-4.

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20

Kozlov, S. M. "Spectral asymptotics of random operators." Mathematical Notes of the Academy of Sciences of the USSR 43, no. 3 (March 1988): 234–43. http://dx.doi.org/10.1007/bf01138848.

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21

Lan, Heng-you. "Approximation solvability of nonlinear random (A,η)-resolvent operator equations with random relaxed cocoercive operators." Computers & Mathematics with Applications 57, no. 4 (February 2009): 624–32. http://dx.doi.org/10.1016/j.camwa.2008.09.036.

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22

Lenczewski, Romuald. "Matricial circular systems and random matrices." Random Matrices: Theory and Applications 05, no. 04 (October 2016): 1650012. http://dx.doi.org/10.1142/s201032631650012x.

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We introduce and study matricial circular systems of operators which play the role of matricial counterparts of circular operators. They describe the asymptotic joint *-distributions of blocks of independent block-identically distributed Gaussian random matrices with respect to partial traces. Using these operators, we introduce circular free Meixner distributions as the non-Hermitian counterparts of free Meixner distributions and construct for them a random matrix model. Our approach is based on the concept of matricial freeness applied to operators on Hilbert spaces. It is closely related to freeness with amalgamation over the algebra [Formula: see text] of [Formula: see text] diagonal matrices applied to operators on Hilbert [Formula: see text]-bimodules.

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23

Beg, Ismat, and Mujahid Abbas. "Random fixed point theorems for Caristi type random operators." Journal of Applied Mathematics and Computing 25, no. 1-2 (September 2007): 425–34. http://dx.doi.org/10.1007/bf02832367.

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24

Jarosz, A., and M. A. Nowak. "Random Hermitian versus random non-Hermitian operators—unexpected links." Journal of Physics A: Mathematical and General 39, no. 32 (July 26, 2006): 10107–22. http://dx.doi.org/10.1088/0305-4470/39/32/s12.

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25

Anh, Pham The. "Random Coincidence Points of Expansive Type Completely Random Operators." Bulletin of the Malaysian Mathematical Sciences Society 38, no. 4 (December 17, 2014): 1609–25. http://dx.doi.org/10.1007/s40840-014-0094-9.

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26

Li, Guozhen, and Huagui Duan. "On random fixed point theorems of random monotone operators." Applied Mathematics Letters 18, no. 9 (September 2005): 1019–26. http://dx.doi.org/10.1016/j.aml.2004.10.006.

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27

Beg, Ismat, and Mujahid Abbas. "Convergence of iterative algorithms to common random fixed points of random operators." Journal of Applied Mathematics and Stochastic Analysis 2006 (September 19, 2006): 1–16. http://dx.doi.org/10.1155/jamsa/2006/89213.

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We prove the existence of a common random fixed point of two asymptotically nonexpansive random operators through strong and weak convergences of an iterative process. The necessary and sufficient condition for the convergence of sequence of measurable functions to a random fixed point of asymptotically quasi-nonexpansive random operators in uniformly convex Banach spaces is also established.

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28

Krutikov, Denis. "Schrödinger Operators with Random Sparse Potentials. Existence of Wave Operators." Letters in Mathematical Physics 67, no. 2 (February 2004): 133–39. http://dx.doi.org/10.1023/b:math.0000032704.88514.9c.

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29

Beg, Ismat, and Naseer Shahzad. "Random fixed point theorems for nonexpansive and contractive-type random operators on Banach spaces." Journal of Applied Mathematics and Stochastic Analysis 7, no. 4 (January 1, 1994): 569–80. http://dx.doi.org/10.1155/s1048953394000444.

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The existence of random fixed points. for nonexpansive and pseudocontractive random multivalued operators defined on unbounded subsets of a Banach space is proved. A random coincidence point theorem for a pair of compatible random multivalued operators is established.

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30

THANG, Dang Hung, and Nguyen THINH. "RANDOM BOUNDED OPERATORS AND THEIR EXTENSION." Kyushu Journal of Mathematics 58, no. 2 (2004): 257–76. http://dx.doi.org/10.2206/kyushujm.58.257.

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31

Lindner, Marko, and Steffen Roch. "Finite Sections of Random Jacobi Operators." SIAM Journal on Numerical Analysis 50, no. 1 (January 2012): 287–306. http://dx.doi.org/10.1137/100813877.

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32

Orlov, Yu N., V. Zh Sakbaev, and O. G. Smolyanov. "Unbounded random operators and Feynman formulae." Izvestiya: Mathematics 80, no. 6 (December 31, 2016): 1131–58. http://dx.doi.org/10.1070/im8402.

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33

Edelman, Alan, and Brian D. Sutton. "From Random Matrices to Stochastic Operators." Journal of Statistical Physics 127, no. 6 (April 18, 2007): 1121–65. http://dx.doi.org/10.1007/s10955-006-9226-4.

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34

Kudlaev, E. M. "Characteristic Operators and Conditioned Random Elements*." Journal of Mathematical Sciences 200, no. 4 (June 28, 2014): 449–51. http://dx.doi.org/10.1007/s10958-014-1927-7.

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35

Kravvaritis, Dimitrios, and Nicolaos Stavrakakis. "Perturbations of maximal monotone random operators." Linear Algebra and its Applications 84 (December 1986): 301–10. http://dx.doi.org/10.1016/0024-3795(86)90322-8.

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36

Bharucha-Reid, A. T. "Random Linear Operators (A. V. Skorohod)." SIAM Review 27, no. 3 (September 1985): 463–64. http://dx.doi.org/10.1137/1027126.

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37

Ueki, Naomasa. "Stochastic analysis and random Schrödinger operators." Sugaku Expositions 31, no. 1 (March 20, 2018): 93–115. http://dx.doi.org/10.1090/suga/430.

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38

Najar, Hatem. "Lifshitz tails for random acoustic operators." Journal of Mathematical Physics 44, no. 4 (April 2003): 1842–67. http://dx.doi.org/10.1063/1.1558902.

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39

Knill, Oliver. "Isospectral deformations of random Jacobi operators." Communications in Mathematical Physics 151, no. 2 (January 1993): 403–26. http://dx.doi.org/10.1007/bf02096774.

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40

Semenov, Mikhail E., Olesia I. Kanishcheva, Peter A. Meleshenko, Olga O. Reshetova, Roman E. Pervezentzev, and Alexander V. Budanov. "On the hysteretic operators with random parameters." MATEC Web of Conferences 241 (2018): 01020. http://dx.doi.org/10.1051/matecconf/201824101020.

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In this work we introduce the novel class of hysteretic operators with random parameters. We consider the definition of these operators in terms of the “input-output” relations, namely: for all permissible continuous inputs corresponds the output in the form of stochastic Markovian process. The properties of such operators are also considered and discussed on the example of a non-ideal relay with random parameters. Application of hysteretic operators with stochastic parameters is demonstrated on the example of simple oscillating system and the results of numerical simulations are presented.

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41

Patriche, Monica. "Random fixed point theorems for lower semicontinuous condensing random operators." Fixed Point Theory 19, no. 1 (February 1, 2018): 369–78. http://dx.doi.org/10.24193/fpt-ro.2018.1.28.

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42

Vishwakarma, Dr Neetu. "Common Random Fixed Point theorem for compatible random multivalued operators." IOSR Journal of Mathematics 3, no. 3 (2012): 39–43. http://dx.doi.org/10.9790/5728-0333943.

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43

Irfan, S. Shakaib, M. Firdosh Khan, Zeid I. Al-Muhiameed, and Carlo Cattani. "On random variational-like inclusion involving relaxed monotone random operators." Cogent Mathematics 4, no. 1 (January 1, 2017): 1305639. http://dx.doi.org/10.1080/23311835.2017.1305639.

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44

Beg, Ismat, and Naseer Shahzad. "Random fixed points of random multivalued operators on polish spaces." Nonlinear Analysis: Theory, Methods & Applications 20, no. 7 (April 1993): 835–47. http://dx.doi.org/10.1016/0362-546x(93)90072-z.

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45

Dhage, Bapurao C. "Multi-valued codensing random operators and functional random integral inclusions." Opuscula Mathematica 31, no. 1 (2011): 27. http://dx.doi.org/10.7494/opmath.2011.31.1.27.

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46

Agarwal, Ravi P., Donal O'Regan, and M. Sambandham. "RANDOM FIXED POINT THEORY FOR MULTIVALUED COUNTABLY CONDENSING RANDOM OPERATORS." Stochastic Analysis and Applications 20, no. 6 (December 31, 2002): 1157–68. http://dx.doi.org/10.1081/sap-120015827.

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47

Thang, Dang Hung, and Pham The Anh. "Some Results on Random Fixed Points of Completely Random Operators." Vietnam Journal of Mathematics 42, no. 2 (October 5, 2013): 133–40. http://dx.doi.org/10.1007/s10013-013-0037-z.

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48

Thang, Dang Hung, and Pham The Anh. "Some results on random coincidence points of completely random operators." Acta Mathematica Vietnamica 39, no. 2 (March 13, 2014): 163–84. http://dx.doi.org/10.1007/s40306-014-0051-6.

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49

Guo, T. X. "Extension Theorems of Continuous Random Linear Operators on Random Domains." Journal of Mathematical Analysis and Applications 193, no. 1 (July 1995): 15–27. http://dx.doi.org/10.1006/jmaa.1995.1221.

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50

Beg, Ismat. "Random fixed points of non-self maps and random approximations." Journal of Applied Mathematics and Stochastic Analysis 10, no. 2 (January 1, 1997): 127–30. http://dx.doi.org/10.1155/s1048953397000154.

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In this paper we prove random fixed point theorems in reflexive Banach spaces for nonexpansive random operators satisfying inward or Leray-Schauder condition and establish a random approximation theorem.

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