Orthonormal polynomial bases in function spaces
- 126 Downloads
We construct polynomial orthonormal bases in various function spaces. Our bases have linear order of growth of degrees of polynomials. We show that this order is optimal.
KeywordsFourier Coefficient Trigonometric Polynomial Polynomial Basis Unconditional Basis ORTHONORMAL Polynomial
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Unable to display preview. Download preview PDF.
- [Boč]S. V. Bočkariov,Construction using Fejer kernels of interpolating dyadic basis in the space of continuous functions, Trudy Steklov Inst.172 (1985), 29–59 (in Russian).Google Scholar
- [Boč2]S. V. Bočkariov,Construction of polynomial bases in finite dimensional spaces of functions analytic in the unit disc, Trudy Steklov Inst.164 (1983), 49–74 (in Russian).Google Scholar
- [Boč3]S. V. Bočkariov,Conjugate Franklin system — a basis in the space of continuous functions, Dokl. Akad. Nauk285 (1985), 521–526 (in Russian).Google Scholar
- [Fab]G. Faber,Über die interpolatorische Darstelung stetige Funktionen, Jahresber. D. M. V.23 (1914), 192–210.Google Scholar
- [Kor]P. P. Korovkin,Linear operators and approximation theory, Fiz.-Mat. Gos. Izdat., Moscow (1959) (in Russian).Google Scholar
- [Sh2]B. Shekhtman,On polynomial “interpolation” in L 1, preprint.Google Scholar
- [S-W]E. M. Stein and G. Weiss,Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, 1971.Google Scholar
- [Ul1]P. L. Ulianov,On some solved and unsolved problems in the theory of orthogonal series, Proc. IV All Union Math. Congress2, Publishing House AN SSSR, Moscow (1964), 694–704 (in Russian).Google Scholar
- [Wo1]P. L. Ulianov,On some results and problems in the theory of bases, Zapiski LOMI, 274–283 (in Russian).Google Scholar
- [Wo2]P. Wojtaszczyk,Banach Spaces for Analysts, Cambridge University Press (to appear).Google Scholar
© Hebrew University 1991