Fredholm and Frame-Preserving Weighted Composition Operators

Bedford, E.: Proper holomorphic mappings. Bull. Am. Math. Soc. 10, 157–175 (1984) Cao, G., He, L., Zhu, K.: Spectral theory of multiplication operators on Hardy–Sobolev spaces. J. Funct. Anal. 275(5), 1259–1279 (2018) Cao, G., He, L., Zhu, K.: Fredholm composition operators and proper holomorphic mappings. Bull. Lond. Math. Soc. 51, 1104–1112 (2019) Christensen, O.: An Introduction to Frames and Riesz Bases. Applied and Numerical Harmonic Analysis, 2nd edn. Birkhäuser-Springer, New York (2016) Douglas, R.: Banach Algebra Techniques in Operator Theory, 2nd edn. Springer, New York (1998) Duffin, R.J., Schaeffer, A.C.: A class of nonharmonic Fourier series. Trans. Am. Math. Soc. 72, 341–366 (1952) Fang, Q., Xia, J.: Corrigendum to multipliers and essential norm on the Drury–Arveson space. Proc. Am. Math. Soc. 141, 363–368 (2013) Forstneric, F.: Proper holomorphic mappings: a survey, Several complex variables. In: Fornaess, J.E. (ed.) Proceedings of the Mittag–Leffler Institute, Mathematical Notes, vol. 38, pp. 297–363. Princeton University Press, Princeton (1993) Manhas, J.S., Prajitura, G.T., Zhao, R.: Weighted composition operators that preserve frames. Integr. Equ. Oper. Theory 91, 34 (2019) Paulsen, V.I., Raghupathi, M.: An Introduction to the Theory of Reproducing Kernel Hilbert Spaces. Cambridge University Press, Cambridge (2016) Richter, S., Sunkes, J.: Hankel operators, invariant subspaces, and cyclic vectors in the Drury–Arveson space. Proc. Am. Math. Soc. 144, 2575–2586 (2016) Rudin, W.: Function Theory in the Unit Ball of \({\mathbb{C} }^n\). Springer, Berlin (1980) Zhao, L.: Fredholm weighted composition operator on weighted Hardy space. J. Funct. Spaces Appl. 2013, 327692 (2013)