@article{Hernández-Eliseo2024, 
author = {Yessica Hernández-Eliseo and Josué Ramírez-Ortega and Francisco G. Hernández-Zamora},
title = {Toeplitz operators on two poly-Bergman-type spaces of the Siegel domain        D    2    ⊂            C        2   with continuous nilpotent symbols},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {3},
pages = {5269-5293},
keywords = {Toeplitz operator, reproducing kernel, poly-analitic functions},
url = {https://www.sciopen.com/article/10.3934/math.2024255},
doi = {10.3934/math.2024255},
abstract = {We studied Toeplitz operators acting on certain poly-Bergman-type spaces of the Siegel domain        D          2        ⊂            C              2      . Using continuous nilpotent symbols, we described the        C    ∗  -algebras generated by such Toeplitz operators. Bounded measurable functions of the form              c      ~        (  ζ  )  =  c  (  Im        ζ          1        ,  Im        ζ          2        −      |        ζ    1              |              2        ) are called nilpotent symbols. In this work, we considered symbols of the form              a      ~        (  ζ  )  =  a  (  Im        ζ    1    ) and              b      ~        (  ζ  )  =  b  (  Im        ζ    2    −      |        ζ    1              |              2        ), where both limits        lim          s      →              0        +              b  (  s  ) and        lim          s      →      +      ∞        b  (  s  ) exist, and    a belongs to the set of piece-wise continuous functions on              R        ¯    =  [  −  ∞  ,  +  ∞  ] and with one-sided limits at    0. We described certain        C    ∗  -algebras generated by such Toeplitz operators that turned out to be isomorphic to subalgebras of        M    n    (      C    )  ⊗  C  (      Π    ¯    ), where        Π    ¯    =            R        ¯    ×                    R            ¯        +   and                      R            ¯        +    =  [  0  ,  +  ∞  ].}
}