Sharp estimates for Jacobi matrices and chain sequences, II |
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Authors: | Ryszard Szwarc |
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Institution: | a Institute of Mathematics, Wroc
aw University, pl. Grunwaldzki 2/4, Wroc
aw 50-384, Poland;b Institute of Mathematics, Polish Academy of Science, ul.
niadeckich 8, Warszawa 00-950, Poland |
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Abstract: | Chain sequences are positive sequences {cn} of the form cn=gn(1−gn−1) for a nonnegative sequence {gn}. They are very useful in estimating the norms of Jacobi matrices and for localizing the interval of orthogonality for orthogonal polynomials. We give optimal estimates for the chain sequences which are more precise than the ones obtained in the paper (Constructive Approx. 6 (1990) 363) and in our earlier paper (J. Approx. Theory 118 (2002) 94). |
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Keywords: | Orthogonal polynomials Chain sequences Jacobi matrices Recurrence relation |
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