General Orthogonal Polynomials

General Orthogonal Polynomials (1992)

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by Vilmos Totik

Venue:	in “Encyclopedia of Mathematics and its Applications,” 43
Citations:	46 - 6 self

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@INPROCEEDINGS{Totik92generalorthogonal,
    author = {Vilmos Totik},
    title = {General Orthogonal Polynomials},
    booktitle = {in “Encyclopedia of Mathematics and its Applications,” 43},
    year = {1992},
    publisher = {University Press}
}

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Abstract

Abstract In this survey, different aspects of the theory of orthogonal polynomials of one (real or complex) variable are reviewed. Orthogonal polynomials on the unit circle are not discussed.

Citations

424	An introduction to orthogonal polynomials - Chihara - 1978
226	Logarithmic Potentials with External Fields - Saff, Totik - 1997
219	Orthogonal Polynomials and Random Matrices: a Riemann– Hilbert Approach - Deift - 1999
171	The Classical Moment Problem and Some Related Questions on Analysis. Translated by N - Akhiezer - 1965
138	Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory - Deift, Kriecherbauer, et al. - 1999
97	Orthogonal polynomials of several variables - Dunkl, Xu - 2001
73	Classical and Quantum Orthogonal Polynomials in One Variable - Ismail - 2005
71	The classical moment problem as a selfadjoint finite difference operator - Simon - 1998
70	Sum rules for Jacobi matrices and their applications to spectral theory - Killip, Simon
69	The isomonodromy approach to matrix models in 2D quantum gravity - Fokas, Its, et al. - 1992
44	Orthogonal polynomials: Computation and approximation - Gautschi - 2004
37	D.: Orthogonal polynomials for exponential weights - Levin, Lubinsky - 2001
33	Orthogonal polynomials - Nevai - 1979
31	Assche, “Asymptotics for orthogonal polynomials - Van - 1987
27	On the asymptotics of the ratio of orthogonal polynomials - Rakhmanov
27	Extremal polynomials associated with a system of curves in the complex plane - Widom - 1969
24	Über Sturm-Liouvillesche Polynomsysteme - Bochner - 1929
24	Sum rules and the Szegő condition for orthogonal polynomials on the real line - Simon, Zlatoˇs
23	Orthogonal polynomials and their zeros - Nevai, Totik - 1989
22	Aptekarev, Multiple orthogonal polynomials - I - 1998
22	On Rakhmanov’s theorem for Jacobi matrices - Denisov
21	The scattering problem for a discrete Sturm– Liouville operator - Aptekarev, Nikishin - 1983
21	Souillard: From power pure point to continuous spectrum in disordered systems, Ann.Inst. H. Poincaré A42 - Delyon, Simon, et al. - 1985
21	Riemann-Hilbert problems for multiple orthogonal polynomials - Assche, Geronimo, et al. - 2001
20	Characterization theorems for orthogonal polynomials, ‘Orthogonal Polynomials: Theory and Practice - Al-Salam - 1990
19	On the trigonometric moment problem - Geronimus - 1946
19	Spectra of random and almost-periodic operators, Grundlehren der Mathematischen Wissenschaften, 297 - Pastur, Figotin - 1992
18	On polynomials orthogonal on the circle, on trigonometric momentproblem and on allied Carathéodory-Schur functions - Geronimus - 1944
16	Orthogonal Polynomials, Akadémiai Kiadó - Freud - 1971
14	Christoffel functions and orthogonal polynomials for Erdos weights - Levin, Lubinsky, et al. - 1994
14	Strong and weak convergence of orthogonal polynomials - Máté, Nevai, et al. - 1987
14	Orthogonal polynomials with complex-valued weight function - Stahl - 1986
13	Strong asymptotics for extremal polynomials associated with weights on - Lubinsky, Saff - 1988
13	On the distribution of zeros of polynomials orthogonal on the unit circle - Mhaskar, Saff - 1990
13	Asymptotics for Christoffel functions for general measures on the real line - Totik
12	A Christoffel-Darboux formula for multiple orthogonal polynomials - Daems, Kuijlaars
11	A survey on orthogonal matrix polynomials satisfying second order differential equations - Durán, Grünbaum
11	Weighted polynomial inequalities with doubling and - Mastroianni, Totik
10	Assche, Scalar and matrix Riemann-Hilbert approach to the strong asymptotics of Padé approximants and complex orthogonal polynomials with varying weight - Aptekarev, Van
10	López Lagomasino: Ratio and relative asymptotics of polynomials orthogonal on an arc of the unit circle - Hernández, M - 1998
10	Szegő’s extremum problem on the unit circle - Máté, Nevai, et al. - 1991
9	Aptekarev, Asymptotic properties of polynomials orthogonal on a system of contours, and periodic motions of Toda chains - I - 1986
9	Extensions of Szegő’s theory of orthogonal polynomials - Máté, Nevai, et al.
9	An Introduction to Orthogonal Polynomials, Mathematics and its applications, v. 13 - Chihara - 1978
8	Zeros and critical points of Sobolev orthogonal polynomials - Gautschi, Kuijlaars - 1997
8	Assche, Orthogonal polynomials on several intervals via a polynomial mapping - Geronimo, Van - 1988
8	Denisov’s theorem on recurrence coefficients - Nevai, Totik
7	Ueber die Entwicklung einer willkürlichen Funktion nach den Nennern des Kettenbruches für - Blumenthal - 1898
7	Zeros of orthogonal polynomials on the real line - Denisov, Simon
7	Asymptotics for Sobolev orthogonal polynomials for exponential weights - Geronimo, Lubinsky, et al.