Geodesic
Weighted Frobenius-Perron operators and their spectra
Mathematica Bohemica, Tome 142 (2017) no. 2, pp. 113-124
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First, some classic properties of a weighted Frobenius-Perron operator $\mathcal {P}_\varphi ^u$ on $L^1(\Sigma )$ as a predual of weighted Koopman operator $W=uU_\varphi $ on $L^\infty (\Sigma )$ will be investigated using the language of the conditional expectation operator. Also, we determine the spectrum of $\mathcal {P}_\varphi ^u$ under certain conditions.
First, some classic properties of a weighted Frobenius-Perron operator $\mathcal {P}_\varphi ^u$ on $L^1(\Sigma )$ as a predual of weighted Koopman operator $W=uU_\varphi $ on $L^\infty (\Sigma )$ will be investigated using the language of the conditional expectation operator. Also, we determine the spectrum of $\mathcal {P}_\varphi ^u$ under certain conditions.
DOI : 10.21136/MB.2016.0079-15
Classification : 11Y50, 47A10, 47B20, 47B38
Keywords: Frobenius-Perron operator; Fredholm operator; spectrum 
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Jabbarzadeh, Mohammad Reza; Hajipouri, Rana. Weighted Frobenius-Perron operators and their spectra. Mathematica Bohemica, Tome 142 (2017) no. 2, pp. 113-124. doi: 10.21136/MB.2016.0079-15

[1] Rao, K. P. S. Bhaskara, Rao, M. Bhaskara: Theory of Charges: A Study of Finitely Additive Measures. Pure and Applied Mathematics 109, Academic Press, London (1983). | MR | JFM

[2] Campbell, J. T., Jamison, J. E.: On some classes of weighted composition operators. Glasg. Math. J. 32 (1990), 87-94 corrigendum on pages 261-263\kern1pt. | DOI | MR | JFM

[3] Ding, J.: A closed range theorem for the Frobenius-Perron operator and its application to the spectral analysis. J. Math. Anal. Appl. 184 (1994), 156-167. | DOI | MR | JFM

[4] Ding, J.: The Frobenius-Perron operator as a product of two operators. Appl. Math. Lett. 9 (1996), 63-65. | DOI | MR | JFM

[5] Ding, J.: The point spectrum of Frobenius-Perron and Koopman operators. Proc. Am. Math. Soc. 126 (1998), 1355-1361. | DOI | MR | JFM

[6] Ding, J., Du, Q., Li, T. Y.: The spectral analysis of Frobenius-Perron operators. J. Math. Anal. Appl. 184 (1994), 285-301. | DOI | MR | JFM

[7] Ding, J., Hornor, W. E.: A new approach to Frobenius-Perron operators. J. Math. Anal. Appl. 187 (1994), 1047-1058. | DOI | MR | JFM

[8] Ding, J., Zhou, A.: On the spectrum of Frobenius-Perron operators. J. Math. Anal. Appl. 250 (2000), 610-620. | DOI | MR | JFM

[9] Ding, J., Zhou, A.: Statistical Properties of Deterministic Systems. Tsinghua University Texts. Springer, Berlin; Tsinghua University Press, Beijing (2009). | DOI | MR | JFM

[10] Jabbarzadeh, M. R.: Weighted Frobenius-Perron and Koopman operators. Bull. Iran. Math. Soc. 35 (2009), 85-96. | MR | JFM

[11] Jabbarzadeh, M. R.: A conditional expectation type operator on $L^p$ spaces. Oper. Matrices 4 (2010), 445-453. | DOI | MR | JFM

[12] Jabbarzadeh, M. R., Emamalipour, H.: Compact weighted Frobenius-Perron operators and their spectra. Bull. Iran. Math. Soc. 38 (2012), 817-826. | MR | JFM

[13] Jabbarzadeh, M. R., Bakhshkandi, M. Jafari: Stability constants for weighted composition operators. To appear in Bull. Belg. Math. Soc.-Simon Stevin.

[14] Rao, M. M.: Conditional Measures and Applications. Pure and Applied Mathematics (Boca Raton) 271, Chapman & Hall/CRC, Boca Raton (2005). | MR | JFM

[15] Yosida, K.: Functional Analysis. Classics in Mathematics. Vol. 123, Springer, Berlin (1995). | DOI | MR | JFM

[16] Zaanen, A. C.: Integration. North-Holland, Amsterdam (1967). | MR | JFM

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