- József Szabados
- … show all 1 hide
The theory of orthogonal polynomials plays an important role in many branches of mathematics, such as approximation theory (best approximation, interpolation, quadrature), special functions, continued fractions, differential and integral equations. The notion of orthogonality originated from the theory of continued fractions, but later became an independent (and possibly more important) discipline. Among the contributors to the theory of orthogonal polynomials, we can find such outstanding mathematicians as Abel, Chebyshev, Fourier, Hermite, Laguerre, Laplace, Legendre, Markov, and Stieltjes, just to name a few. Beginning with Gábor Szegő, Hungarian mathematicians like Pál Erdös, Pál Turán, Géza Freud, Ervin Feldheim and others have made essential contributions to the flourishing theory of orthogonal polynomials in the last century. At this point I would like to mention two names who have made considerable efforts to propagate the work of the above mentioned Hungarian mathematicians: Richard Askey and Doron Lubinsky.
- Freud, Géza, Orthogonale Polynome, Akadémiai Kiadó (Budapest), Birkhäuser (Basel, 1969). Orthogonal Polynomials, Pergamon Press (London-Toronto-New York, 1971).
- Grenander, Ulf — Szegő, Gábor, Toeplitz Forms and their Applications, University of California Press (Berkeley and Los Angeles, 1958)/Chelsea (New York, 1984).
- Saff, Edward B. — Totik, Vilmos, Logarithmic Potentials with External Fields, Grundlehren der Mathematischen Wissenschaften, Vol. 316, Springer-Verlag (Berlin-New York, 1997).
- Szegő, Gábor, Collected Papers, ed. R. Askey, Birkhäuser (Boston-Basel-Stuttgart, 1982).
- Szegő, Gábor, Orthogonal Polynomials, American Mathematical Society Colloquium Publications, Vol. XXIII., 1939, revised 1959, 3rd edition 1967, 4th edition 1975.
- Totik, Vilmos, Weighted Approximation with Varying Weight, Springer Lecture Notes in Mathematics, No. 1569, Springer-Verlag (Berlin-New York, 1994).
- P. Nevai, Orthogonal Polynomials, Memoirs Amer. Math. Soc., 213 (1979), 1–185.
- Orthogonal Polynomials
- Book Title
- A Panorama of Hungarian Mathematics in the Twentieth Century I
- pp 55-70
- Print ISBN
- Online ISBN
- Series Title
- Bolyai Society Mathematical Studies
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- eBook Packages
To view the rest of this content please follow the download PDF link above.