The Bergman kernel on forms: General theory
Author:
Andrew Raich
Journal:
Proc. Amer. Math. Soc. 146 (2018), 4683-4692
MSC (2010):
Primary 32A25, 32A55, 32W05
DOI:
https://doi.org/10.1090/proc/13921
Published electronically:
August 14, 2018
MathSciNet review:
3856137
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: The goal of this paper is to explore the Bergman projection on forms. In particular, we show that some of most basic facts used to construct the Bergman kernel on functions, such as pointwise evaluation in , fail for
-forms,
,
. We do, however, provide a careful construction of the Bergman kernel and explicitly compute the Bergman kernel on
-forms. For the ball in
, we also show that the size of the Bergman kernel on
-forms is not governed by the control metric, in stark contrast to the Bergman kernel on functions.
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Additional Information
Andrew Raich
Affiliation:
Department of Mathematical Sciences, SCEN 309, University of Arkansas, Fayetteville, Arkansas 72701
Email:
araich@uark.edu
DOI:
https://doi.org/10.1090/proc/13921
Keywords:
Bergman projection,
Bergman kernel
Received by editor(s):
June 2, 2017
Received by editor(s) in revised form:
July 20, 2017
Published electronically:
August 14, 2018
Additional Notes:
The author was partially supported by NSF grant DMS-1405100.
Communicated by:
Harold P. Boas
Article copyright:
© Copyright 2018
American Mathematical Society