Abstract
In this paper, we study properties of composition operators on the Newton space, i.e., the Hilbert space of analytic functions which have the Newton polynomials as an orthonormal basis. In particular, we focus on various properties of the composition operator \(C_{T}\) induced by T on the Newton space where \(T(z)=z+1\). Moreover, we examine conditions on the symbol \(\varphi \) for the induced composition operator \(C_{\varphi }\) which belongs to Newton space \(N^{2}({{\mathbb {P}}})\) where \(\varphi \) is a linear fraction transformation or an analytic function of \({\mathbb P}\). Finally, we concern complex symmetric composition operators on the Newton space \(N^{2}({{\mathbb {P}}})\).
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References
Aiena, P.: Fredholm and Local Spectral Theory with Applications to Multipliers. Kluwer Academic Pub, New York (2004)
de Branges, L., Trutt, D.: Quantum Ces\(\grave{a}\)ro operators. In: Gohberg, T., Kac, M. (eds.)Topics in Functional Analysis (Essays dedicated to M. G. Krein), Adv. in Math. Suppl. Studies, vol. 3. Academic Press, New York, pp. 1–24 (1978)
Garcia, S.R., Putinar, M.: Complex symmetric operators and applications. Trans. Am. Math. Soc. 358, 1285–1315 (2006)
Garcia, S.R., Prodan, E., Putinar, M.: Mathematical and physical aspects of complex symmetric operators. J. Phys. A Math. Th. 47, 1–51 (2014)
Greene, R.E., Krantz, S.G.: Function Theory of on Complex Variable, vol. 40, 2nd edn. Graduate Studies in Mathematics, Amer. Math. Soc
Han, K.: Complex symmetric composition operators on the Newton space. J. Math. Anal. Appl. 488, 124091 (2020)
Ko, E., Lee, J.E.: On complex symmetric Toeplitz operators. J. Math. Anal. Appl. 434, 20–34 (2016)
Ko, E., Lee, J.E.: Remark on complex symmetric operator matrices. Lin. Multi. Alg. 67(6), 1198–1216 (2019)
Kay, E., Trutt, D.L.: Newton spaces of analytic functions. J. Math. Anal. Appl. 60, 325–328 (1978)
Kriete, T.L., Trutt, D.: The Cesaro operator in is subnormal. Am. J. Math. 93, 215–225 (1971)
Kriete, T.L., Trutt, D.: On the Ces\(\grave{a}\)ro operator. Indiana U. Math. J. 24, 197–214 (1974)
MacDonald, G., Rosenthal, P.: Composition operators on the Newton space. J. Funct. Anal. 260, 2518–2540 (2011)
Markett, C., Rosenblum, M., Rovnyak, J.: A Plancherel theory for Newton spaces. Int. Eq. Op. Th. 9, 831–862 (1986)
Wang, X., Gao, Z.: A note on Aluthge transforms of complex symmetric operators and applications. Int. Eq. Op. Th. 65, 573–580 (2009)
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The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (no. 2019R1F1A1058633) the Ministry of Education (no. 2019R1A6A1A11051177). The second author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (no. 2019R1A2C1002653). The third author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (no. 2021R1C1C1008713).
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Ko, E., Lee, J.E. & Lee, J. Remarks on Composition Operators on the Newton Space. Mediterr. J. Math. 19, 205 (2022). https://doi.org/10.1007/s00009-022-02130-2
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DOI: https://doi.org/10.1007/s00009-022-02130-2