Premium
Pseudospectra and holomorphic functions of matrices
Author(s) -
Ransford Thomas,
Raouafi Samir
Publication year - 2013
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bds104
Subject(s) - holomorphic function , mathematics , constant (computer programming) , transformation (genetics) , pure mathematics , mathematical analysis , combinatorics , computer science , chemistry , biochemistry , gene , programming language
Does there exist a constant M = M ( f , N ) such that || f ( A )|| ⩽ M || f ( B )|| whenever A , B are N × N matrices with identical pseudospectra? We show that the answer is ‘yes’ if f is a Möbius transformation, and ‘no’ for all other non‐constant holomorphic functions f (provided N ⩾ 6).
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom