TY - JOUR
T1 - Fourier representations in Bergman spaces
AU - Chakrabarti, Debraj
AU - Upadrashta, Pranav
N1 - Funding Information:
We would like to thank Sivaram Narayan and David Barrett for their helpful comments. We would also like to thank the referee for helpful suggestions leading to improvement of the paper. Research of the first author was supported by a National Science Foundation grant ( DMS-1600371 ), and by a collaboration grant from the Simons Foundation (# 316632 ).
Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2019/7/1
Y1 - 2019/7/1
N2 - We consider a class of domains, generalizing the upper half-plane, and admitting rotational, translational and scaling symmetries analogous to the half-plane. We prove Paley-Wiener type representations of functions in Bergman spaces of such domains with respect to each of these three groups of symmetries. The Fourier series, Fourier integral and Mellin integral representations so obtained may be used to give representations of the Bergman kernels of these domains.
AB - We consider a class of domains, generalizing the upper half-plane, and admitting rotational, translational and scaling symmetries analogous to the half-plane. We prove Paley-Wiener type representations of functions in Bergman spaces of such domains with respect to each of these three groups of symmetries. The Fourier series, Fourier integral and Mellin integral representations so obtained may be used to give representations of the Bergman kernels of these domains.
KW - Bedford-Pinchuk eggs
KW - Bergman space
KW - Holomorphic Fourier transforms
KW - Paley-Wiener representations
UR - http://www.scopus.com/inward/record.url?scp=85062262297&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2019.02.050
DO - 10.1016/j.jmaa.2019.02.050
M3 - Article
AN - SCOPUS:85062262297
SN - 0022-247X
VL - 475
SP - 464
EP - 489
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -