Personal Research

My research revolves around problems at the intersection of operator theory and complex analysis. In particular the focus is on using Hilbert spaces of holomorphic functions (such as the Hardy, Dirichlet and Bergman spaces) and the spectral theory of their operators as tools to investigate seemingly unrelated problems in operator-related function theory and analytic number theory.

Publications

  1. (with Aditya Ghosh, Kobi Kremnizer and Charles F. Santos) Zero-free half-planes of the ζ-function via spaces of analytic functions, Adv. Math. 455 (2024) 109872
  2. (with João R. Carmo and Ben Hur Eidt) Minimal invariant subspaces for an affine composition operator, Complex Anal. Oper. Theory 18, 59 (2024). https://doi.org/10.1007/s11785-024-01501-9.
  3. (with Juan Manzur and Charles F. Santos) A weighted composition semigroup related to three open problems, J. Math. Anal. Appl. 525(2023) 127261.
  4. (with João R. Carmo) Universal composition operators, J. Operator Theory, 87 (2022) 137-156.
  5. (with Osmar R. Severiano) Interplay between complex symmetry and Koenigs eigenfunctions, J. Math. Anal. Appl. 500 (2021) 125111.
  6. (with Osmar R. Severiano) Complex symmetry and cyclicity of composition operators on H2(C+), Proc. Amer. Math. Soc. 148 (2020), 2469-2476.
  7. A Hardy space analysis of the Báez-Duarte criterion for the RH, Adv. Math. 350 (2019) 242-255.
  8. Complex symmetry of Toeplitz operators with continuous symbols, Arch. Math. 109 (2017), 455–460.
  9. On an example of a complex symmetric composition operator on H^2(D), J. Funct. Anal., 269 (2015), pp. 1899-1901.
  10. (with Paul Bourdon) Complex symmetry of invertible composition operators, J. Math. Anal. Appl. 429 (2015) 105–110.
  11. Complex symmetry of composition operators induced by involutive ball automorphisms, Proc. Amer. Math. 142 (2014), no. 9, 3103–3107.
  12. (with Dan Timotin) Embeddings of Müntz spaces: the Hilbertian case, Proc. Amer. Math. Soc. 141 (2013), no. 6, 2009–2023.
  13. Embeddings of Müntz spaces: composition operators, Integr. Equ. Oper. Theory 73, 589–602 (2012).

Latest Preprints

  1. (with Francisco Calderaro, Juan Manzur and Charles F. Santos) Orthogonality questions in the Hardy space related to ζ-zeros, Preprint.
  2. (with Pham Viet Hai and Osmar Reis Severiano) Composition operators on Paley-Wiener spaces, Preprint.
  3. (with Ben Hur Eidt) Beurling and Model subspaces invariant under a universal operator, Preprint.
  4. (with Marcos Ferriera) Universal Toeplitz operators on the Hardy space over the polydisk, Preprint.