Geodesic
Stability condition and Riesz bounds for exponential splines
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1430-1442
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Stability of the family of integer translations of exponential spline $U_{m,p}$ for arbitrary $m,p$ is proven; Riesz bounds are determined. The method presented in the paper allows to calculate Riesz bounds for the convolution of a B-spline of an arbitrary order and a function with an appropriated Fourier transform.
Keywords: E-spline, Riesz basis, Riesz bounds, functional series. 
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E. V. Mishchenko. Stability condition and Riesz bounds for exponential splines. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1430-1442. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a67/

[1] I.J. Schoenberg, “Contributions to the problem of approximation of equidistant data by analytic functions. Part A: On the problem of smoothing or graduation. A first class of analytic approximation formulae”, Q. Appl. Math., 4 (1946), 45–99 | DOI | MR | Zbl

[2] I.J. Schoenberg, “Contributions to the problem of approximation of equidistant data by analytic functions. Part B: On the problem of osculatory interpolation. A second class of analytic approximation formulae”, Q. Appl. Math., 4 (1946), 112–141 | DOI | MR | Zbl

[3] I.J. Schoenberg, “On trigonometric spline interpolation”, J. Math. Mech., 13:5 (1964), 795–825 | MR | Zbl

[4] L.L. Schumaker, Spline functions: basic theory, Wiley-Interscience, New York etc, 1981 | MR | Zbl

[5] H.G. ter Morsche, Interpolation and extremal properties of L-splines functions, Dissertation, Technishe Hogeschool Eindhoven, Eindhoven, 1982 | MR | Zbl

[6] L.L. Schumaker, “On hyperbolic splines”, J. Approxim. Theory, 38:2 (1983), 144–166 | DOI | MR | Zbl

[7] A.Y. Bezhaev, V.A. Vasilenko, “Variational spline theory”, Bull. Novosib. Comput. Cent., Ser. Numer. Anal., 1993, no. 3, Novosibirsk, 1993 | MR | Zbl

[8] M.A. Unser, “Splines: a perfect fit for medical imaging”, Medical Imaging 2002: Image Processing (9 May 2002), Proc. SPIE, 4684, 2002 | DOI

[9] O.E. Hepson, A. Korkmaz, I. Dag, “Exponential B-spline collocation solutions to the Gardner equation”, Int. J. Comput. Math., 97:4 (2020), 837–850 | DOI | MR | Zbl

[10] Ch.K. Chui, An introduction to wavelets, Academic Press, Boston, 1992 | MR | Zbl

[11] E.V. Mishchenko, “Determination of Riesz bounds for the spline basis with the help of trigonometric polynomials”, Sib. Math. J., 51:4 (2010), 660–666 | DOI | MR | Zbl