Implicit Gamma Theorems (I): Pseudoroots and Pseudospectra

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机构：
[1] MIP,
[2] Département de Mathématique Université Paul Sabatier 31062 Toulouse Cedex 04,undefined
[3] France dedieu@mip.ups-tlse.fr,undefined
[4] Department of Mathematics SUNY at Old Westbury Old Westbury,undefined
[5] NY 11568-0210,undefined
[6] USA kimm@oldwestbury.edu,undefined
[7] IBM T. J. Watson Research Center PO Box 218 Yorktown Heights,undefined
[8] NY 10532,undefined
[9] USA mshub@us.ibm.com,undefined
[10] Department of Mathematics University of Manchester Manchester M13 9PL,undefined
[11] England ftisseur@ma.man.ac.uk,undefined
来源：
Foundations of Computational Mathematics | 2003年 / 3卷
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AMS Classification. 65F15, 65H10, 65Y20.;
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摘要：
Abstract. Let g : E → F be an analytic function between two Hilbert spaces E and F. We study the set g(B(x, ε)) ⊂ E, the image under g of the closed ball about x∈E with radius ε . When g(x) expresses the solution of an equation depending on x , then the elements of g(B(x,ε )) are ε -pseudosolutions. Our aim is to investigate the size of the set g(B(x,ε )) . We derive upper and lower bounds of the following form:
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页码：1 / 31
页数：30
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