Characterizations of symmetrized polydisc

Sushil Gorai () and Jaydeb Sarkar ()
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Sushil Gorai: Indian Institute of Science Education and Research
Jaydeb Sarkar: Statistics and Mathematics Unit

Indian Journal of Pure and Applied Mathematics, 2016, vol. 47, issue 3, 391-397

Abstract: Abstract Let Γ n , n ≥ 2, denote the symmetrized polydisc in ℂ n , and Γ1 be the closed unit disc in ℂ. We provide some characterizations of elements in Γ n . In particular, an element (s 1,..., s n−1, p) ∈ ℂ n is in Γ n if and only if $${s_j} = {\beta _j} + \overline {{\beta _{n - j}}}p$$ s j = β j + β n − j ¯ p , j = 1,..., n − 1, for some (β 1,..., β n−1) ∈ Γ n−1, and |p| ≤ 1.

Keywords: Symmetrized polydisc; Schur theorem; positive definite matrix (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s13226-016-0174-7

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