Abstract
In the paper, we construct a system of smooth two-dimensional splines and describe a class of measures for which this system is a basis in the Sobolev weight space on the square.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Z. Ciesielski, “A construction of basis inC (1)(I 2),”Studia Math.,33, No. 2, 243–247 (1969).
S. Schonefeld, “Schauder bases in spaces of differentiable functions,”Bull. Amer. Math. Soc.,75, 589–590 (1969).
Z. Ciesielski and J. Domsta, “Construction of orthonormal basis inC m(I d) andW mp (I d),”Studia Math.,41, No. 2, 211–224 (1972).
H. B. Carry and I. J. Schoenberg, “On Polya frequence function. IV,”J. Anal. Math.,17, 71–107 (1966).
Boor C. de, “Splines as linear combinations ofB-splines,” in:Approximation Theory, Vol. II, Acad. Press, New York (1976), pp. 1–47.
A. A. Akopyan and A. A. Saakyan, “Multidimensional splines and polynomial interpolation,”Uspekhi Mat. Nauk [Russian Math. Surveys],48, No. 5, 3–76 (1993).
Boor C. de, “The quasi-interpolant as a tool in elementary spline theory,” in:Approximation Theory, Acad. Press, New York (1973), pp. 269–276.
N. I. Akhiezer,Lectures in Approximation Theory [in Russian], Nauka, Moscow (1965).
A. M. Olevskii,Fourier Series with Respect to General Orthogonal Systems, Springer, Berlin (1975).
Author information
Authors and Affiliations
Additional information
Translated fromMatematicheskie Zametki, Vol. 67, No. 3, pp. 343–354, March, 2000.
Rights and permissions
About this article
Cite this article
Demenko, V.N. Bases in Sobolev weight spaces. Math Notes 67, 286–295 (2000). https://doi.org/10.1007/BF02676664
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02676664