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2018 Multivariable isometries related to certain convex domains
Ameer Athavale
Rocky Mountain J. Math. 48(1): 19-46 (2018). DOI: 10.1216/RMJ-2018-48-1-19

Abstract

Several interesting results exist in the literature on subnormal operator tuples having their spectral properties tied to the geometry of strictly pseudoconvex domains or to that of bounded symmetric domains in $\mathbb{C} ^n$. We introduce a class $\Omega ^{(n)}$ of convex domains in $\mathbb{C} ^n$ which, for $n \geq 2$, is distinct from the class of strictly pseudoconvex domains and the class of bounded symmetric domains and which lends itself to the application of theories related to the abstract inner function problem and the $\overline \partial $-Neumann problem, allowing us to make a number of interesting observations about certain subnormal operator tuples associated with the members of the class $\Omega ^{(n)}$.

Citation

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Ameer Athavale. "Multivariable isometries related to certain convex domains." Rocky Mountain J. Math. 48 (1) 19 - 46, 2018. https://doi.org/10.1216/RMJ-2018-48-1-19

Information

Published: 2018
First available in Project Euclid: 28 April 2018

zbMATH: 06866698
MathSciNet: MR3795731
Digital Object Identifier: 10.1216/RMJ-2018-48-1-19

Subjects:
Primary: 47B20

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 1 • 2018
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