Toeplitz operators on the weighted Bergman spaces of quotient domains

@article{78325,
   author = {Ghosh, Gargi and Narayanan, E K},
   article_location = {Amsterdam, Netherlands},
   article_number = {november},
   doi = {http://dx.doi.org/10.1016/j.bulsci.2023.103340},
   keywords = {Toeplitz operator; Pseudorelfection group; Quotient domain; Weighted Bergman space},
   language = {eng},
   issn = {0007-4497},
   journal = {Bulletin des Sciences Mathématiques},
   title = {Toeplitz operators on the weighted Bergman spaces of quotient domains},
   url = {https://www.sciencedirect.com/science/article/pii/S0007449723001148},
   volume = {188},
   year = {2023}
}

TY  - JOUR
ID  - 78325
AU  - Ghosh, Gargi - Narayanan, E K
PY  - 2023
TI  - Toeplitz operators on the weighted Bergman spaces of quotient domains
JF  - Bulletin des Sciences Mathématiques
VL  - 188
IS  - november
SP  - "103340-1"-"103340-29"
EP  - "103340-1"-"103340-29"
PB  - Elsevier
SN  - 00074497
KW  - Toeplitz operator
KW  - Pseudorelfection group
KW  - Quotient domain
KW  - Weighted Bergman space
UR  - https://www.sciencedirect.com/science/article/pii/S0007449723001148
N2  - Let G be a finite pseudoreflection group and omega subset of Cd be a bounded domain which is a G-space. We establish identities involving Toeplitz operators on the weighted Bergman spaces of omega and omega/G using invariant theory and representation theory of G. This, in turn, provides techniques to study algebraic properties of Toeplitz operators on the weighted Bergman space on omega/G. We specialize on the generalized zero-product problem and characterization of commuting pairs of Toeplitz operators. As a consequence, more intricate results on Toeplitz operators on the weighted Bergman spaces on some specific quotient domains (namely symmetrized polydisc, monomial polyhedron, Rudin's domain) have been obtained.
ER  - 

GHOSH, Gargi and E K NARAYANAN. Toeplitz operators on the weighted Bergman spaces of quotient domains. \textit{Bulletin des Sciences Mathématiques}. Amsterdam, Netherlands: Elsevier, 2023, vol.~188, november, p.~''103340-1''-''103340-29'', 29 pp. ISSN~0007-4497. Available from: https://dx.doi.org/10.1016/j.bulsci.2023.103340.