Double condensation of singularities for Walsh-Fourier series

Ştefan Cobzaş

Authors

Ştefan Cobzaş "Babeş-Bolyai" University, Cluj-Napoca, Romania

Abstract views: 240

Abstract

Not available.

Downloads

Download data is not yet available.

References

V. Anisiu, A principle of double condensation of singularities using the σ-porosity. Seminar on Mathematical Analysis, Babeş-Bolyai University, Cluj-Napoca, Preprint 7 (1985), pp. 85-88.

P. Billard, Sur la convergence presque partout des séries de Fourier-Walsh des fonctions de l'espace L²[0,1], Studia Math. 28 (1967), pp. 363-388.

W. W. Breckner, Eine Verallgemeinerung des Prinzips der gleichmässigen Beschränktkeit,, Mathematica - Rev. Anal. Numér. Théorie Approximation, 9 (1980), pp. 11-18.

W. W. Breckner, A principle of condensation of singularities for set-valued functions. Mathematica - Rev. Anal. Numér, Théorie Approximation 12 (1983), pp. 101-111.

W. W. Breckner, Condensation and double condensation of the singularities of families of numerical functions, Proc. Colloq. Appox. Optimiz., Univ. Cluj-Napoca, 1985, pp. 201-212.

L. Carleson, On convergence and growth of partial sums of Fourier series, Acta Math. 116 (1966), pp. 135-157.

S. Cobzas, I. Muntean, Condensation of singularities and divergence reulst in approximation theory, J. Approx. theory 31 (1981), pp. 138-153 https://doi.org/10.1016/0021-9045(81)90038-1.

N. J. Fine, On the Walsh functions, Trans. Amer. Math. Soc. 65 (1949), pp. 372-414 https://doi.org/10.2307/1990619

V. Golubov, A. Efimov, V. Skvortsov, Walsh Series and Transofrmations, Mathematics and its Applications, Soviet Series 64, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991.

E. Hewitt, K. A. Ross, Abstract Harmonic Analysis, Vol. I, 2nd ed. (1972), Vol. II (1970), Springer V., Berlin -Heidelberg - New York.

E. Hewitt, K. Stromberg, Real and Abstract Analysis, Springer - V. Berlin - Heidelberg - New York, 1965.

P. Jebelean, On the dense divergence of Lagrange interpolation in the complex domain, Mathematica - Rev. Anal. Numér. Théorie Approximation, 12 (1983), pp. 61-64.

P. Jebelean, Double condensation of singularities for symmetric mappings, Studia Univ. Babeş-Bolyai, Ser. Math. 20 (1984), pp. 47-52.

J. L. Kelley, General Topology. Van Nostrand, New York, 1957.

I. Kolumban, Des Prinzip der Kondensation der Singularitáten prákonvexer Funktionen. Mathematica - Rev. Anal. Numér. Théorie Approximation 9 (1980), pp. 59063.

I. Mitrea, On the condensation of singularities of Lagrange interpolation processes on saturated sets. Seminar on Mathematical analysis, Babeş-Bolyai Univ. (Cluj-Napoca), Preprint 4 (1986), pp. 71-78.

I. Mitrea, The topological structure of the set of unbounded divergence for some approximation methods. Proc. Second Symposium of Mathematics and its Applications, Timişoara, 1987, pp. 98-1-2.

I. Mitrea, On the unbounded divergence in mean of Lagrange interpolation porocesses for extended node matrices, Seminar on Mathematical Analysis, Babeş-Bolyai Univ. (Cluj-Napoca), Preprint 7 (1987), pp. 81-90.

I. Mitrea, On the unbounded divergence of numerical differentiation for equidistant nodes. Seminar on Mathematical Analysis, Babeş-Bolyai Univ. (Cluj-Napoca), Preprint 6 (1988), pp. 227-232.

I. Muntean, Unbounded divergence of simple quadrature formulas, J. Approx. Theory 67 (1991), pp. 303-310. https://doi.org/10.1016/0021-9045(91)90005-U

L. Nachbin, the Hear Integral, Van Nostrand Princeton, N. J., 1965.

R. E. A. C. Paley, A remarkable system of orthogonal functions. Proc. London Math. Soc. 34 (1932), pp. 241-279 https://doi.org/10.1112/plms/s2-34.1.241

W. Rudin, Fourier Analysis on Groups, Interscience, New York - London 1962.

W. Rudin, Real an Complex analysis, McGraw-Hill, New York 1966.

F. Schipp, W. R. Wade, P. Simon, Walsh Series. An Introduction to Dyadie Harmonic Analysis, Akadémiai Kiadó, Budapest 1990.

A. A. Achneider, On series with respect to Walsh functions with monotone coefficients. Izv. Akad. Nauk SSSR, Ser. Mat. 19 (1948), pp. 179-192.

N. Ja. Vilenkin, A class of complete orthonormal series, Izv. Akad. Nauk SSSR Ser. Mat. 11 (1947), pp. 363-400.

J. L. Walsh, A closed set of normal orthogonal functions, Amer. J. Math. 45 (1923), pp. 5-24 https://doi.org/10.2307/2387224