Browsing by Author "Poon, Yiu-Tung"

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MINKOWSKI PRODUCT OF CONVEX SETS AND PRODUCT NUMERICAL RANGE
(2016-12)
Li, Chi-Kwong
;
Pelejo, Diane Christine
;
Poon, Yiu-Tung
;
Wang, Kuo-Zhong
;
應用數學系
Let K-1, K-2 be two compact convex sets in C. Their Minkowski product is the set K1K2 = {ab : a is an element of K-1, b is an element of K-2}. We show that the set K1K2 is star-haped if K-1 is a line segment or a circular disk. Examples for K-1 and K-2 are given so that K-1 and K-2 are triangles (including interior) and K1K2 is not star-shaped. This gives a negative answer to a conjecture by Puchala et. al concerning the product numerical range in the study of quantum information science. Additional results and open problems are presented.
MINKOWSKI PRODUCT OF CONVEX SETS AND PRODUCT NUMERICAL RANGE
(2016-12)
Li, Chi-Kwong
;
Pelejo, Diane Christine
;
Poon, Yiu-Tung
;
Wang, Kuo-Zhong
;
應用數學系
Let K-1, K-2 be two compact convex sets in C. Their Minkowski product is the set K1K2 = {ab : a is an element of K-1, b is an element of K-2}. We show that the set K1K2 is star-haped if K-1 is a line segment or a circular disk. Examples for K-1 and K-2 are given so that K-1 and K-2 are triangles (including interior) and K1K2 is not star-shaped. This gives a negative answer to a conjecture by Puchala et. al concerning the product numerical range in the study of quantum information science. Additional results and open problems are presented.