Research

Research Interests:
  1. Complex Analysis
  2. Operator Theory
PhD Students:

  • Krishna Subedi (2018)
  • Anthony Vasaturo (2018)
  • Bhupendra Paudyal (2014)
  • Amila Appuhamy (2013)
  • Mehdi Nikpour (2012)

    • Publications:
    1. (with Jari Taskinen) A geometric condition for the invertibility of Toeplitz operators on the Bergman space, to appear in Studia Math.
    2. (with Jari Taskinen) Pointwise lower bounds in growth spaces with little o-conditions, Math. Scand. 131 (2025), no. 2, 320-332
    3. (with Timothy G. Clos and Sonmez Sahutoglu) Compactness of composition operators on the Bergman space of the bidisc, Integral Equations Operator Theory 97 (2025), no. 3, Paper No. 21
    4. (with Sonmez Sahutoglu and Zhenghui Huo) On spectra of Hankel operators on the polydisc, Canad. Math. Bull. 68 (2025), no. 1, 301-317
    5. (with Sonmez Sahutoglu and Zhenghui Huo) Zero products of Toeplitz operators on Reinhardt domains, Can. Math. Bull. 65 (2022), 170-179
    6. (with Michael Stessin and Alexandre Tchernev) Determinantal hypersurfaces and representations of Coxeter groups, Pacific J. Math.313 (2021), 103-125
    7. Projected composition operators on pseudoconvex domains, Integral Equations Operator Theory 93 (2021), Paper number 35, 11pp.
    8. (with Sonmez Sahutoglu) Berezin regularity of domains in $\mathbb{C}^n$ and the essential norms of Toeplitz operators Trans. Amer. Math. Soc.  374  (2021),  no. 4, 2521-2540
    9. (with Sonmez Sahutoglu and Yunus Zeytuncu) A local weighted Axler-Zheng theorem in  $\mathbb{C}^n$, Pacific J. Math.  294  (2018),  no. 1, 89-106
    10. (with Anthony Vasaturo) Carleson measures and Douglas' question on the Bergman space, to appear in Rend. Circ. Mat. Palermo (2)  67  (2018),  no. 2, 323-336
    11. (with Bhupendra Paudyal) The lattices of invariant subspaces of a class of operators on the Hardy space Arch. Math. (Basel) 110 (2018),  no. 5, 477-486
    12. (with Raul Curto) A new necessary condition for the hyponormality of Toeplitz operators on the Bergman space, J. Operator Theory  79  (2018),  no. 2, 287-300
    13. (with Sonmez Sahutoglu) Essential norm estimates for the $\overline{\partial}$-Neumann operator on convex domains and worm domains, Indiana Univ. Math. J.  67  (2018),  no. 1, 267-292
    14. Estimates of the $L^p$ norms of the Bergman projection on strongly pseudoconvex domains, Integral Equations Operator Theory 88 (2017), 331-338
    15. (with Sonmez Sahutoglu) Essential norm estimates for Hankel operators on convex domains in $\mathbb{C}^2$, Math. Scand. 120 (2017), 305-316
    16. (with Yunus Zeytuncu) Mapping properties of weighted Bergman projection operators on Reinhardt domains, Proc. Amer. Math. Soc. 144 (2016), no. 8, 3479-3491
    17. (with Trieu Le) Adjoints of linear fractional composition operators on weighted Hardy spaces, Acta Sci. Math. (Szeged) 82 (2016), no. 3-4, 651-662
    18. (with Bhupendra Paudyal) Invariant subpaces of the shift plus complex Volterra operator, J. Math. Anal. Appl. 426 (2015), no. 2 1174-1181
    19. (with Sonmez Sahutoglu) Compactness of products of Hankel operators on convex Reinhardt  domains in $\mathbb{C}^2$, , New York J. Math. 20 (2014), 627-643
    20. (with Trieu Le) Toeplitzness of composition operators in several variables, Complex Var. Elliptic Equ. 59 (2014), no.10, 1351-1362
    21. (with Sonmez Sahutoglu) Axler-Zheng type theorem on a class of domains in Cn, Integral Equations Operator Theory 77 (2013), no. 3, 397-405
    22. (with Mehdi Nikpour) On the Toeplitzness of the adjoint of composition operators, J. Math. Anal. Appl. 408 (2013), no. 2 541-546
    23. (with Trieu Le) Toeplitz operators on Bergman spaces of polyanalytic functions, Bull. London Math. Soc. 44 (2012), no. 5, 961-973
    24. (with Bo Li) Berezin transform, Mellin transform and Toeplitz operators, Complex Anal. Oper. Theory 6 (2012), no. 1, 189-218
    25. (with Sonmez Sahutoglu) Compactness of products of Hankel operators on the polydisk and some product domains in $\mathbb{C}^2$, J. Math. Anal. Appl. 371 (2010), 341-346
    26. (with Sonmez Sahutoglu) Compactness of Hankel operators and analytic discs in the boundary of pseudoconvex domains, J. Funct. Anal. 256 (2009), no. 11, 3730-3742
    27. (with Issam Louhichi) Finite rank commutators and semicommutators of quasihomogeneous Toeplitz operators, Complex Anal. Oper. Theory 2 (2008), no. 3, 429-439
    28. Finite rank perturbations of Toeplitz operators, Integral Equations Operator Theory 59 (2007), no. 3, 345--353
    29. (with Ruhan Zhao) Weighted composition operators between different weighted Bergman spaces and different Hardy space, Illinois J. Math. 51 (2007), no. 2, 479--498
    30. (with Ruhan Zhao) Essential norm estimates of weighted composition operators between Bergman spaces on strongly pseudoconvex domains, Math. Proc. Cambridge Philos. Soc. 142 (2007), no. 3, 525-533
    31. (with Jeffery D. McNeal) Special Toeplitz operators on strongly pseudoconvex domains, Rev. Mat. Iberoam. 22 (2006), no. 3, 851-866
    32. (with N.V. Rao) Maximality theorems for Frechet algebras, Proc. Amer. Math. Soc. 134 (2006), no. 2, 487-490
    33. (with Joseph A. Cima) Compact Toeplitz operators with unbounded symbols, J. Operator Theory 53 (2005), no. 2, 431-440
    34. (with Ruhan Zhao) Weighted composition operators on the Bergman space, J. London Math. Soc. (2) 70 (2004), no. 2, 499-511
    35. (with Patrick Ahern) Some examples related to the Brown-Halmos theorem for the Bergman space, Acta Sci. Math. (Szeged) 70 (2004), no. 1-2, 373-378 
    36. Berezin versus Mellin, J. Math. Anal. Appl. 287 (2003), no. 1, 234-243
    37. (with Nasser Towghi) Sample paths of α-chaos, J. Math. Anal. Appl. 264 (2001), no. 2, 682-686 
    38. (with Patrick Ahern)  A theorem of Brown-Halmos type for Bergman space Toeplitz operators, J. Funct. Anal. 187 (2001), no. 1, 200-210
    39. (with Patrick Ahern) Products of Toeplitz operators on the Bergman space, Illinois J. Math. 45 (2001), no. 1, 113-121
    40. (with Sheldon Axler and N.V. Rao) Commutants of analytic Toeplitz operators on the Bergman space, Proc. Amer. Math. Soc. 128 (2000), no. 7, 1951-1953
    41. (with Kit C. Chan) $C^*$-algebras generated by a subnormal operator, Trans. Amer. Math. Soc. 351 (1999), no. 4, 1445-1460
    42. (with N.V. Rao)  Mellin transform, monomial symbols, and commuting Toeplitz operators, J. Funct. Anal. 154 (1998), no. 1, 195-214
    43. Commuting Toeplitz operators on the Bergman space of an annulus, Michigan Math. J. 43 (1996), no. 2, 355-365
    44. (with Patrick Ahern) A mean value inequality with applications to Bergman space operators, Pacifiic J. Math. 173 (1996), no. 2, 295-305
    45. (with Da Shan Fan) Commutants of Toeplitz operators on the ball and annulus, Glasgow Math. J. 37 (1995), no. 3, 303-309
    46. (with Patrick Ahern) An invariant submean value property and hyponormal Toeplitz operators, Harmonic analysis and operator theory (Caracas, 1994), 17-24, Contemp. Math., 189, Amer. Math. Soc., Providence, RI, 1995
    47. Commutants of Toeplitz operators on the Bergman space, Pacific J. Math. 162 (1994), no. 2, 277-285 
    48. (with Sheldon Axler) Commuting Toeplitz operators with harmonic symbols, Integral Equations Operator Theory 14 (1991), no. 1, 1-12