References
G. Szegő,Orthogonal Polynomials, AMS Coll. Publ. Vol.23 (Providence, Rhode Island, 1959).
E. M. Stein, B. Muckenhoupt, Classical expansions and their relation to conjugate harmonic functions,Trans. Amer. Math. Soc.,118 (1965), 17–92.
B. Muckenhoupt, Poisson integrals for Hermite and Laguerre expansions,Trans. Amer. Math. Soc.,139 (1969), 231–242.
B. Muckenhoupt, Hermite conjugate expansions,Trans. Amer. Math. Soc.,139 (1969), 243–260.
B. Muckenhoupt, Conjugate functions for Laguerre expansions,Trans. Amer. Math. Soc.,147 (1970), 403–418.
G. Alexits, Sur l'ordre de grandeur de l'approximation d'une fonction périodique par les sommes de Fejér,Acta Math. Acad. Sci. Hung.,3 (1952), 29–40.
I. Joó, On the order of approximation by Fejér means of Hermite-Fourier and Laguerre-Fourier series,Acta Math. Hung.,61 (1988), 365–370.
I. Joó, Saturation theorems for Hermite-Fourier series,Acta Math. Hung.,57 (1991).
I. Joó, On the divergence of eigenfunction expansions,Annales Univ. Sci. Budapest. Sectio Math.,32 (1989), 3–36.
A. Bogmér, Generalisation of a theorem of G. Alexits,Annales Univ. Sci. Budapest. Sectio Math.,31 (1988), 223–228.
M. Horváth, Some saturation theorems for classical orthogonal expansions. I,Periodica Math. Hung. (to appear).
P. L. Butzer, H. Berens,Semigroups of Operators and Approximation, Springer (Berlin, 1967).
J. Garnett,Bounded Analytic Functions, Academic Press (New-York, 1981).
S. Banach, Sur la convergence presque partout de fonctionnelles linéaires,Bull. Sci. Math.,50 (1926), 27–32, 36–43.
E. L Poiani, Mean Cesàro summability of Laguerre and Hermite series,Trans. Amer. Math. Soc.,193 (1972), 1–31.
P. L. Butzer, R. J. Nessel, W. Trebels, On summation processes of Fourier expansions in Banach spaces III: Jackson- and Zamansky-type inequalities for Abel-bounded expansions,Tôhoku Math. J.,27 (1975), 213–223.
W. Trebels,Multipliers for (C, α)-bounded Fourier expansions in Banach spaces and approximation theory, Lecture Notes in Math. 329, Springer (Berlin, 1973).
I. Joó, On some problems of M. Horváth,Annales Univ. Sci. Budapest. Sectio Math.,31 (1988), 243–260.
M. H. Stone, A generalized Weierstrass approximation theorem,Studies in Modern Analysis (Studies in Math. 1, Ed. R. C. Buck), Amer. Math. Soc. Prentice Hall, 1962.
P. L. Butzer, R. J. Nessel,Fourier Analysis and Approximation, Vol. I. Birkhäuser (Basel, 1971).
I. Joó, On Hermite-Fourier series, Preprint of the Math. Inst. of the Hung. Acad. of Sci. No 12/1987;Per. Math. Hung. (to appear).
I. Joó, On Hermite-conjugate function,Annales Univ. Sci. Budapest. Sectio Math.,33 (1990) (to appear).
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Horváth, M. Some saturation theorems for classical orthogonal expansions. II. Acta Math Hung 58, 157–191 (1991). https://doi.org/10.1007/BF01903558
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DOI: https://doi.org/10.1007/BF01903558