Finite-infinite range inequalities in the complex plane
Let E⫅C be closed, ω be a suitable weight function on E, σ be a positive Borel measure on E. We discuss the conditions on ω and σ which ensure the existence of a fixed compact subset K of E with the following property. For any p, 0<P≤∞, there exist positive constants c1, c2 depending only on E, ω...
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| Format: | Article |
| Language: | English |
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Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171291000868 |
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| author | H. N. Mhaskar |
| author_facet | H. N. Mhaskar |
| author_sort | H. N. Mhaskar |
| collection | DOAJ |
| description | Let E⫅C be closed, ω be a suitable weight function on E, σ be a positive
Borel measure on E. We discuss the conditions on ω and σ which ensure the existence of
a fixed compact subset K of E with the following property. For any p, 0<P≤∞, there
exist positive constants c1, c2 depending only on E, ω, σ and p such that for every integer
n≥1 and every polynomial P of degree at most n,
∫E\K|ωnP|pdσ≤c1exp(−c2n)∫K|ωnP|pdσ.
In particular, we shall show that the support of a certain extremal measure is, in some
sense, the smallest set K which works. The conditions on σ are formulated in terms of
certain localized Christoffel functions related to σ. |
| format | Article |
| id | doaj-art-3087ea6ac0d847e3b01c8760544c4319 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1991-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3087ea6ac0d847e3b01c8760544c43192025-02-03T01:24:18ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114462563810.1155/S0161171291000868Finite-infinite range inequalities in the complex planeH. N. Mhaskar0Department of Mathematics, California State University, Los Angeles 90032, California, USALet E⫅C be closed, ω be a suitable weight function on E, σ be a positive Borel measure on E. We discuss the conditions on ω and σ which ensure the existence of a fixed compact subset K of E with the following property. For any p, 0<P≤∞, there exist positive constants c1, c2 depending only on E, ω, σ and p such that for every integer n≥1 and every polynomial P of degree at most n, ∫E\K|ωnP|pdσ≤c1exp(−c2n)∫K|ωnP|pdσ. In particular, we shall show that the support of a certain extremal measure is, in some sense, the smallest set K which works. The conditions on σ are formulated in terms of certain localized Christoffel functions related to σ.http://dx.doi.org/10.1155/S0161171291000868finite-infinite range inequalitiesorthogonal polynomials weighted polynomialsNikolskii inequalities. |
| spellingShingle | H. N. Mhaskar Finite-infinite range inequalities in the complex plane International Journal of Mathematics and Mathematical Sciences finite-infinite range inequalities orthogonal polynomials weighted polynomials Nikolskii inequalities. |
| title | Finite-infinite range inequalities in the complex plane |
| title_full | Finite-infinite range inequalities in the complex plane |
| title_fullStr | Finite-infinite range inequalities in the complex plane |
| title_full_unstemmed | Finite-infinite range inequalities in the complex plane |
| title_short | Finite-infinite range inequalities in the complex plane |
| title_sort | finite infinite range inequalities in the complex plane |
| topic | finite-infinite range inequalities orthogonal polynomials weighted polynomials Nikolskii inequalities. |
| url | http://dx.doi.org/10.1155/S0161171291000868 |
| work_keys_str_mv | AT hnmhaskar finiteinfiniterangeinequalitiesinthecomplexplane |