 

Shubham R. Bais and
D. Venku Naidu
Integral representation of angular operators on the Bergman space
over the upper halfplane
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print


Published: 
January 16, 2024. 
Keywords: 
Bergman space, Multiplication operator, Reducing subspace, Toeplitz operator, Angular operator, Fourier transform. 
Subject [2010]: 
30H20, 47A15, 47B35, 47G10, 42A45. 


Abstract
In this article, we consider a class of integral operators on the Bergman
space over the upper halfplane. We characterize the integral kernels so
that the operators are bounded. We show that the collection of all such
bounded integral operators coincide with the wellknown class of angular
operators. In other words, we provide integral representation for the class of
angular operators. In terms of the integral representation, we study various
operator theoretic properties of angular operators. Also, we give integral
representation for all operators in the C*algebra generated by Toeplitz
operators with angular defining symbols.


Acknowledgements
The first author thanks the University Grant Commission (UGC), India for providing financial support. The authors thank the editor for helpful suggestions and pointing out missing references. The authors also thank the referee(s) for meticulously reading our manuscript and giving us several valuable suggestions which improved the clarity of the paper.


Author information
Shubham R. Bais
Department of Mathematics
Indian Institute of Technology  Hyderabad
Kandi, Sangareddy, Telangana 502284, India
shubhambais007@gmail.com
D. Venku Naidu
Department of Mathematics
Indian Institute of Technology  Hyderabad
Kandi, Sangareddy, Telangana 502284, India
venku@math.iith.ac.in

