Journal of Operator Theory
Volume 88, Issue 2, Fall 2022 pp. 479-510.
Hypercontractions and factorizations of multipliers in one and several variables
Authors:
Monojit Bhattacharjee (1), B. Krishna Das (2), Jaydeb Sarkar (3)
Author institution:(1) Department of Mathematics, Birla Institute of
Technology and Science -Pilani, K.K. Birla Goa Campus, Goa, 403726, India
(2) Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India
(3) Indian Statistical Institute, Statistics and Mathematics Unit, 8th Mile, Mysore Road, Bangalore, 560059, India
Summary: We introduce the notion of characteristic functions
for commuting tuples of hypercontractions on Hilbert spaces,
as a generalization of the notion of Sz.-Nagy and Foias
characteristic functions of contractions.
We pre\-sent an explicit method to compute characteristic functions
of hypercontractions and relate characteristic functions
by means of the factors of Schur--Agler class of functions
and universal multipliers on the unit ball in $\mathbb{C}^n$.
We also offer some factorization properties
of multipliers. Characteristic functions of hypercontrations
are a complete unitary invariant. The Drury--Arveson space and the weighted
Bergman spaces on the unit ball continue to play a significant role
in our consideration. Our results are new even in the special case of single hypercontractions.
DOI: http://dx.doi.org/10.7900/jot.2021apr01.2362
Keywords: hypercontractions, weighted Bergman spaces, Bergman
inner functions, analytic models, characteristic functions,
factorizations of multipliers, joint invariant subspaces
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