Cite

Leon Brown, Invertible elements in the Dirichlet space. Canad. Math. Bull., 33(4):419-422, 1990. Search in Google Scholar

Leon Brown and William Cohn. Some examples of cyclic vectors in the Dirichlet space. Proc. Amer. Math. Soc., 95(1):42-46, 1985. Search in Google Scholar

Leon Brown and Allen L. Shields. Cyclic vectors in the Dirichlet space. Trans. Amer. Math. Soc., 285(1):269-303, 1984. Search in Google Scholar

Joseph A. Cima, Alec L. Matheson, and William T. Ross. The Cauchy transform, volume 125 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2006. Search in Google Scholar

Douglas N. Clark. One dimensional perturbations of restricted shifts. J. Analyse Math., 25:169-191, 1972. Search in Google Scholar

Constantin Costara and Thomas Ransford. Which de Branges-Rovnyak spaces are Dirichlet spaces (and vice versa)? J. Funct. Anal., 265(12):3204-3218, 2013. Search in Google Scholar

Louis de Branges and James Rovnyak. Square summable power series. Holt, Rinehart and Winston, New York-Toronto, Ont.-London, 1966. Search in Google Scholar

Ronald G. Douglas, Harold S. Shapiro, and Allen L. Shields. On cyclic vectors of the backward shift. Bull. Amer. Math. Soc., 73:156-159, 1967. Search in Google Scholar

Peter L. Duren. Theory of Hp spaces. Academic Press, New York, 1970. Search in Google Scholar

Omar El-Fallah, Youssef Elmadani, and Karim Kellay. Cyclicity and invariant subspaces in Dirichlet spaces. J. Funct. Anal., 270(9):3262-3279, 2016. Search in Google Scholar

Omar El-Fallah, Karim Kellay, and Thomas Ransford. Cyclicity in the Dirichlet space. Ark. Mat., 44(1): 61-86, 2006. Search in Google Scholar

Omar El-Fallah, Karim Kellay, and Thomas Ransford. On the Brown-Shields conjecture for cyclicity in the Dirichlet space. Adv. Math., 222(6):2196-2214, 2009. Search in Google Scholar

Emmanuel Fricain, Andreas Hartmann, and William T. Ross. Concrete examples of H (b) spaces. Comput. Methods Funct. Theory, 16(2):287-306, 2016. Search in Google Scholar

Emmanuel Fricain, Andreas Hartmann, and William T. Ross. Range spaces of co-analytic Toeplitz operators. Canad. J. Math., 70(6):1261-1283, 2018. Search in Google Scholar

Emmanuel Fricain, Andreas Hartmann, and William T. Ross. Multipliers between range spaces of coanalytic Toeplitz operators. Acta Sci. Math. (Szeged), 85(1-2):215-230, 2019. Search in Google Scholar

Emmanuel Fricain and Javad Mashreghi. Boundary behavior of functions in the de Branges-Rovnyak spaces. Complex Anal. Oper. Theory, 2(1):87-97, 2008. Search in Google Scholar

Emmanuel Fricain and Javad Mashreghi. The theory of ℋ(b) spaces. Vol. 1, volume 20 of New Mathematical Monographs. Cambridge University Press, Cambridge, 2016. Search in Google Scholar

Emmanuel Fricain and Javad Mashreghi. The theory of ℋ(b) spaces. Vol. 2, volume 21 of New Mathematical Monographs. Cambridge University Press, Cambridge, 2016. Search in Google Scholar

Emmanuel Fricain, Javad Mashreghi, and Daniel Seco. Cyclicity in non-extreme de Branges-Rovnyak spaces. In Invariant subspaces of the shift operator, volume 638 of Contemp. Math., pages 131-136. Amer. Math. Soc., Providence, RI, 2015. Search in Google Scholar

Stephan Ramon Garcia, Javad Mashreghi, and William T. Ross. Introduction to model spaces and their operators, volume 148 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2016. Search in Google Scholar

John B. Garnett. Bounded analytic functions, volume 96 of Pure and Applied Mathematics. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. Search in Google Scholar

Caixing Gu, Shuaibing Luo, and Stefan Richter. Higher order local Dirichlet integrals and de Branges Rovnyak spaces. Adv. Math., 385:Paper No. 107748, 47, 2021. Search in Google Scholar

Håkan Hedenmalm and Allen Shields. Invariant subspaces in Banach spaces of analytic functions. Michigan Math. J., 37(1):91-104, 1990. Search in Google Scholar

Karim Kellay and Mohamed Zarrabi. Two-isometries and de Branges-Rovnyak spaces. Complex Anal. Oper. Theory, 9(6):1325-1335, 2015. Search in Google Scholar

Nikolai K. Nikolski. Operators, functions, and systems: an easy reading. Vol. 1, volume 92 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2002. Hardy, Hankel, and Toeplitz, Translated from the French by Andreas Hartmann. Search in Google Scholar

Stefan Richter and Carl Sundberg. Multipliers and invariant subspaces in the Dirichlet space. J. Operator Theory, 28(1):167-186, 1992. Search in Google Scholar

Donald Sarason. Doubly shift-invariant spaces in H2. J. Operator Theory, 16(1):75-97, 1986. Search in Google Scholar

Donald Sarason. Sub-Hardy Hilbert spaces in the unit disk, volume 10 of University of Arkansas Lecture Notes in the Mathematical Sciences. John Wiley & Sons, Inc., New York, 1994. A Wiley-Interscience Publication. Search in Google Scholar