symmetrized polydisc
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2021 ◽  
pp. 2150036
Author(s):  
Sourav Pal ◽  
Samriddho Roy

We find new characterizations for the points in the symmetrized polydisc [Formula: see text], a family of domains associated with the spectral interpolation, defined by [Formula: see text] We introduce a new family of domains which we call the extended symmetrized polydisc [Formula: see text], and define in the following way: [Formula: see text] [Formula: see text] We show that [Formula: see text] for [Formula: see text] and that [Formula: see text] for [Formula: see text]. We first obtain a variety of characterizations for the points in [Formula: see text] and we apply these necessary and sufficient conditions to produce an analogous set of characterizations for the points in [Formula: see text]. Also, we obtain similar characterizations for the points in [Formula: see text], where [Formula: see text]. A set of [Formula: see text] fractional linear transformations plays central role in the entire program. We also show that for [Formula: see text], [Formula: see text] is nonconvex but polynomially convex and is starlike about the origin but not circled.





2018 ◽  
Vol 356 (4) ◽  
pp. 387-394
Author(s):  
Guicong Su ◽  
Yanyan Tang ◽  
Zhenhan Tu




2016 ◽  
Vol 47 (3) ◽  
pp. 391-397
Author(s):  
Sushil Gorai ◽  
Jaydeb Sarkar
Keyword(s):  


2015 ◽  
Vol 10 (5) ◽  
pp. 921-941 ◽  
Author(s):  
Nikolai Nikolov ◽  
Pascal J. Thomas ◽  
Duc-Anh Tran
Keyword(s):  


2013 ◽  
Vol 141 (7) ◽  
pp. 2361-2370 ◽  
Author(s):  
Gadadhar Misra ◽  
Subrata Shyam Roy ◽  
Genkai Zhang


2008 ◽  
Vol 341 (1) ◽  
pp. 140-148 ◽  
Author(s):  
Nikolai Nikolov ◽  
Peter Pflug ◽  
Pascal J. Thomas ◽  
Włodzimierz Zwonek


2007 ◽  
Vol 135 (09) ◽  
pp. 2921-2929 ◽  
Author(s):  
Nikolai Nikolov ◽  
Peter Pflug ◽  
Wlodzimierz Zwonek


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