TY  - BOOK
AU  - Levin,A.L.
AU  - Lubinsky,D.S.
TI  - Christoffel Functions and Orthogonal Polynomials for Exponential Weights on 
T2  - Memoirs of the American Mathematical Society
SN  - 9781470401146
AV  - QA404.5 -- .L485 1994eb 
U1  - 515/.55 
PY  - 1994///
CY  - Providence
PB  - American Mathematical Society
KW  - Orthogonal polynomials
KW  - Christoffel-Darboux formula
KW  - Convergence
KW  - Electronic books
N1  - Intro -- Table of Contents -- 1. Introduction and Results -- Definition 1.1: The class W -- Theorem 1.2: Christoffel Functions -- Corollary 1.3: Sup-Norms of Christoffel Functions -- Corollary 1.4: Zeros -- Corollary 1.5: Bounds on Orthonormal Polynomials -- Theorem 1.6: Sup-Norm Christoffel Functions -- Theorem 1.7: Restricted Range Inequalities -- Theorem 1.8: L[sub(p)] Norms of Orthonormal Polynomials -- 2. Some Ideas Behind the Proofs -- I. An Orthogonal Polynomial Angle -- II. The Potential Theory Side: Lower Bounds for λ[sub(n)] -- III. The Potential Theory Side: Upper Bounds for λ[sub(n)] -- IV. The Orthogonal Polynomials Angle: An(x) -- 3. Technical Estimates -- Lemma 3.1: Estimates involving Q -- Lemma 3.2: Estimates involving α[sub(u)] -- Lemma 3.3: More estimates involving α[sub(u)] -- Lemma 3.4: Estimates for Δ[sub(n)](s,t) -- Lemma 3.5: Differences involving Δ[sub(n)](s,t) -- 4. Estimates for the Density Functions μ[sub(n)] -- Lemma 4.1: Old estimates for μ[sub(n)] -- Theorem 4.2: Estimates for μ[sub(n)] on all of („1,1) -- Theorem 4.3: Differences involving μ[sub(n)] -- Proof of Theorem 4.2 -- Proof of Theorem 4.3 (b) -- Proof of Theorem 4.3 (a) -- 5. Majorization Functions and Integral Equations -- Lemma 5.1: Old Potential Theory/Integral Equations -- Lemma 5.2: Estimates for B[sub(n,R)],v[sub(n,R)] -- Theorem 5.3: Estimates for U[sub(n,R)] -- 6. The Proof of Theorem 1.7 -- Lemma 6.1: L[sub(p)] Bounds for Weighted Polynomials -- Proof of Theorem 1.7 -- 7. Lower Bounds for λ[sub(n)] -- Theorem 7.1: Lower Bounds for μ[sub(n)] -- Lemma 7.2: Preliminary Lower Bounds -- Proof of Theorem 7.1 -- 8. Discretisation of a Potential: Theorem 1.6 -- Theorem 8.1: One Point Polynomials -- Deduction of Theorem 1.6 -- Theorem 8.2: The Bounds for Γ[sub(n)] -- Deduction of Theorem 8.1 -- Lemma 8.3: Estimates for the discretisation points; Lemma 8.4: Estimates for S[sub(1)]+[sub(4)] -- Lemma 8.5: Estimates for μ[sub(j)] -- Lemma 8.6: Estimates for τ[sub(j)] -- Lemma 8.7: Estimates for S[sub(21)] -- Lemma 8.8: Lower Bounds for S[sub(2)] -- Lemma 8.9: Upper Bounds for S[sub(2)] -- Lemma 8.10: Bounds for S[sub(3)] -- Proof of Theorem 8.2 -- 9. Upper Bounds for λ[sub(n)]: Theorems 1.2 and Corollary 1.3 -- Lemma 9.1: Preliminary Upper Bounds for μ[sub(n)] -- Proof of Theorem 1.2 -- Proof of Corollary 1.3 -- 10. Zeros: Corollary 1.4 -- Proof of Corollary 1.4 (i) -- Lemma 10.1: Series Equivalent to wω[sup(…2)] -- Proof of a Weaker Form of Corollary 1.4 (ii) -- 11. Bounds on Orthogonal Polynomials: Corollary 1.5 -- Lemma 11.1: An Identity for P'[sub(n)](x[sub(jn)]) -- Lemma 11.2: A Bound for I[sub(1)] -- Lemma 11.3: An Integral Estimate -- Lemma 11.4: An Estimate for I[sub(2)] -- Lemma 11.5: An Estimate for I[sub(3)] -- Theorem 11.6: Implicit Bounds for A[sub(n)] -- Proof of the Upper Bounds for Orthogonal Polynomials -- Lemma 11.7: A Further Integral Estimate -- Theorem 11.8: Good Estimates for A[sub(n)] -- Proof of Corollary 1.5 (iii) -- Lemma 11.9: A Markov-Bernstein Inequality -- Proof of the Lower Bounds for Orthogonal Polynomials -- 12. L[sub(p)] Norms of Orthonormal Polynomials: Theorem 1.8 -- Upper Bounds for L[sub(p)] Norms of Orthonormal Polynomials -- Lemma 12.2: Fundamental Polynomials of Interpolation -- Lower Bounds for L[sub(p)] Norms of Orthonormal Polynomials -- Proof of Corollary 1.4 (ii) -- References
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