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Convergence Conditions for Vector Stieltjes Continued Fractions

โœ Scribed by M.Castro Smirnova


Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
142 KB
Volume
115
Category
Article
ISSN
0021-9045

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Generalizations of S leszyn ski Pringheim's convergence criteria for ordinary continued fractions are proved for noncommutative continued fractions in Banach spaces. Some of them are exact generalizations of the scalar results.

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Let F F be the family of continued fractions K a r1 , where a s yg , a s g x , ps2, 3, . . . , with 0 F g F 1, g fixed, and x F 1, p s py 1 p p p p p 2, 3, . . . . In this work, we derive upper bounds on the errors in the convergents of ลฝ . K a r1 that are uniform for F F, and optimal in the sense