03705nam 2200613 450 991048061200332120180613001258.01-4704-0114-2(CKB)3360000000464719(EBL)3113936(SSID)ssj0000888821(PQKBManifestationID)11453144(PQKBTitleCode)TC0000888821(PQKBWorkID)10865679(PQKB)10803194(MiAaPQ)EBC3113936(PPN)195414187(EXLCZ)99336000000046471920140909h19941994 uy 0engur|n|---|||||txtccrChristoffel functions and orthogonal polynomials for exponential weights on [₋1, 1] /A. L. Levin, D. S. LubinskyProvidence, Rhode Island :American Mathematical Society,1994.©19941 online resource (166 p.)Memoirs of the American Mathematical Society,0065-9266 ;Number 535"September 1994, Volume 111, Number 535 (fourth of 5 numbers)."0-8218-2599-2 Includes bibliographical references.""Table of Contents""; ""Â1. 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""; ""Â2. Some Ideas Behind the Proofs""; ""I. An Orthogonal Polynomial Angle""; ""II. The Potential Theory Side: Lower Bounds for λ[sub(n)]""""Proof of Theorem 4.2""""Proof of Theorem 4.3 (b)""; ""Proof of Theorem 4.3 (a)""; ""Â5. 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)]""; ""Â6. The Proof of Theorem 1.7""; ""Lemma 6.1: L[sub(p)] Bounds for Weighted Polynomials""; ""Proof of Theorem 1.7""; ""Â7. Lower Bounds for λ[sub(n)]""; ""Theorem 7.1: Lower Bounds for Î?[sub(n)]""; ""Lemma 7.2: Preliminary Lower Bounds""; ""Proof of Theorem 7.1""""Â8. Discretisation of a Potential: Theorem 1.6""""Theorem 8.1: One Point Polynomials""; ""Deduction of Theorem 1.6""; ""Theorem 8.2: The Bounds for Î?[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 Î?[sub(j)]""; ""Lemma 8.6: Estimates for Ï?[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""""Lemma 11.5: An Estimate for I[sub(3)]""Memoirs of the American Mathematical Society ;Number 535.Orthogonal polynomialsChristoffel-Darboux formulaConvergenceElectronic books.Orthogonal polynomials.Christoffel-Darboux formula.Convergence.515/.55Levin A. L.1944-768216Lubinsky D. S(Doron Shaul),1955-MiAaPQMiAaPQMiAaPQBOOK9910480612003321Christoffel functions and orthogonal polynomials for exponential weights on2218894UNINA