Christoffel functions and orthogonal polynomials for Erd¨os weights on (–∞,∞)
We establish bounds on orthonormal polynomials and Christoffel functions associated with weights on IR of the form W2 = e−2Q, where Q : IR → IR is even, and is of faster than polynomial growth at ∞ (so-called Erd¨os weights). Typical examples are Q(x) := expk |x| α1, α > 1, , where expk = expk (...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Sapienza Università Editrice
1994-01-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
| Subjects: | |
| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1994(2)/199-289.pdf |
| Summary: | We establish bounds on orthonormal polynomials and Christoffel functions associated with weights on IR of the form W2 = e−2Q, where Q : IR → IR is even,
and is of faster than polynomial growth at ∞ (so-called Erd¨os weights). Typical examples are Q(x) := expk |x| α1, α > 1, , where expk = expk (exp (... exp(·))) denotes
the kth iterated exponential. Further, we obtain uniform estimates on the spacing of
all the zeros and on the Christoffel functions. These results complement earlier ones
for the case where Q is of polynomial growth at ∞ (so-called Freud weights) and for
exponential weights on (−1, 1).
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| ISSN: | 1120-7183 2532-3350 |